Before I get started, I should warn you that this deck won't be everyone's cup of tea. I mean that in two ways: firstly, it plays cards that are pretty much universally seen as terrible (*cough* Nozdormu *cough*), and also, it wins by abusing a mechanic that many might consider to be unfair or unintended.
This is arguably the most powerful combo currently in existence. The combo works by abusing Nozdormu's time-reducing effect with slow animations that take longer than your turn. Once you have Nozdormu in play, play a Youthful Brewmaster, followed by another Youthful Brewmaster targeting the first one. Then repeat that action as many times as possible before your turn ends. Once your rope explodes, the Brewmaster animations will continue. Your opponent won't be allowed to begin their turn until all the animations have finished, which will take up their whole 15 second turn. On your next turn, repeat the process. By doing this, you prevent your opponent from ever having a turn. On each of your turns, in addition to frantically chaining the pandas together, just attack with Nozdormu. In a few turns your opponent will be dead, and there's not a darn thing they can do about it. To get a better idea of how to pull off the combo, check out this example video:
Yes, this combo is pretty degenerate, and I'm not here to defend it or claim that it's fair. I just figure that if this mechanic works, we may as well figure out the best way to utilise it. In some ways this is the first 'pure' combo deck in Hearthstone. Traditional HS combo decks are really just synergy decks, utilising card interactions to provide a burst of damage. This combo deck reminds me of old-school broken combo decks from MtG, where 2 or 3 cards interacted in such a way that they provide an infinite loop that literally wins the game immediately. So here's my build of the deck. Try it out if you're interested, and post your thoughts or suggestions for improvements in the comments. Perhaps if more people try it and it gets enough attention, Blizzard might be more inclined to finally change Nozdormu so that the animations don't eat into the opponent's turn.
Despite being a combo deck, you want to avoid getting any of the combo pieces in your opening hand. That's because the combo won't work until the very late game, and unlike normal HS combos, you can't afford to waste any of the combo pieces earlier in the game. The early game usually plays out like a standard Rogue control deck. The cards you want to mulligan for are things that will help you stabilise. Mulligan away Nozdormu, Youthful Brewmasters, Conceals, and usually Emperor Thaurissan. Backstab, Eviscerate, SI:7 Agent, Deadly Poison, and Blade Flurry are all important in the early game to kill your opponent's minions and make sure you last long enough to pull off the combo later, so hold onto those cards. In some matchups, such as against Druids, hold onto Sap to bounce fat minions, but usually you won't want Sap until the mid-game.
Spend the first few turns trying to keep the board as clear as possible. Try not to waste your Wicked Knife by pinging the opponent unless you're sure that you can afford to use your hero power again next turn, because you might need to have a full dagger to power up with Deadly Poison next turn. Remember that when the combo works as it should, your opponent's life total will be irrelevent, because the combo effectively 'goes infinite'. You should still get in there for easy damage when you're sure it's safe (when you know you can use your hero power again afterwards), because some games you will win without needing the combo. But be mindful of using your Wicked Knife as a resource.
In the mid-game you keep playing like a traditional Rogue deck. Azure Drakes are great to power up your spells, but more importantly, they draw you closer to your combo. Don't be too conservative about throwing them down, even if you know they'll get killed, because at that point in the game getting to your combo is more important. Loatheb can be used whenever you think it's tactically advantageous. Preparation into Sprint should hopefully get you the rest of your combo. If you can follow that up with Emperor Thaurissan, you're golden, but the Emperor isn't strictly necessary for the combo, so again don't be afraid to just run him out as bait or to trade if necessary. If you need more time to dig for the combo, gain some health with Antique Healbot, repeated with Shadowstep if you need to.
At this stage in the game, the only combo piece that you can safely burn is a duplicate Conceal if you have both of them already. A mid-game Conceal can sometimes solidify your lead and make the combo unnecessary. Because the combo is built into the shell of a standard Rogue mid-range/control deck, you will probably find that you win just as many games with the combo as you do without it. An added bonus of this deck is that sometimes a naked Nozdormu (without the combo) against Grim Patron Warrior will wreck the Patron player because all the Frothing Berserker animations will take too long!
Once you've got 10 mana and all the combo pieces in your hand (or earlier if you got lucky with Emperor Thaurissan), play Nozdormu followed by Conceal for protection. At this point your opponent will have a one turn window to kill you, but if they can't do it, you should effectively win next turn. Next turn, you will need another minion in play (it doesn't matter which one) before you play the Youthful Brewmaster, then start jamming out the Brewmasters targeting each other as fast as possible. This will take some practice. As soon as you target one panda with another, its border will light up green, before the animation process moves it back to your hand. Immediately click it and target the other panda, and repeat that as many times as possible. Do NOT wait for the Brewmasters to return to your hand before re-playing them, otherwise you will burn through your own 15 second turn waiting for the animations, which defeats the whole point of the deck. Attack with Nozdormu each turn, but don't bother attacking with any smaller minions that you happen to have in play. You're better off spending that time repeatedly clicking on the Youthful Brewmasters. As soon as the Brewmaster animations finish, the game will flick back to your next turn, without giving your opponent time to take a turn. Attack with Nozdormu again and get back to clicking pandas. Repeat until victorious.
Note: It's possible to overdose on animations. Once you've mastered all the fast clicking, you might be able to bounce the Youthful Brewmasters 5 times in one turn, or even add more actions. Don't do it! The animations will take so long that you'll skip not just the opponent's turn, but also your next turn. That means that after that your opponent will get a full 15 second turn, which will probably be your undoing. So be careful to only trigger the pandas enough to skip the opponent's turn, without eating into your next turn's 15 seconds. 3 or 4 triggers each turn seems to be the sweet spot. Any more than that is counterproductive or fatal.
Obviously Nozdormu is irreplacable. It may feel pathetic to waste 1600 dust on such a bad card, but of course this combo won't work without it. The other legendaries in the deck are less important though, because they're not central to the combo. You could replace Bloodmage Thalnos with a Loot Hoarder or Kobold Geomancer. Card draw is usually more important than spell damage, so I'd prefer the Loot Hoarder. Loatheb and Emperor Thaurissan are really just there for value, so they could be replaced with any other high-value minions that you have available. Other legendaries would fit well, such as Sylvanas Windrunner or Edwin VanCleef, or even just Piloted Shredders if you don't have access to legendaries.
I've built the combo into a basic mid-range/control Rogue shell, but there are various alternative options you could try. Because the core of the deck is so small (just Nozdormu and the Brewmasters) it could be slotted into most existing Rogue decks. Oil Rogue would potentially be a good option, but I feel that Oil Rogue is already so refined that cutting anything from it would probably reduce its win percentage. So the other build I'd consider is a hybrid of the Nozdormu combo and Mill Rogue. That would give you access to Coldlight Oracle (probably replacing Azure Drake) for extra card draw.
Let me know what you think about this deck in the comments. Personally, I think this combo is ridiculous, and shouldn't be part of the game. I'm hoping that bringing more attention to it will pressure Blizzard into fixing Nozdormu. So give the deck a try if you're interested, and give it a +1 so that more people see it and discuss it. If enough people see it and play it and discuss it, hopefully this will help to get the mechanic fixed quicker.