Hearthpwn

In E.T.C., Band Manager's Band, you put Potion of Illusion, and as his Band-cards are not considered to start in your deck, it is replayed on Grand Magister Rommath when you play him afterward. That, together with Time Warp, easily gives you 5+ turns in a row, and not rarely way more, even though rarely necessary.

The other two Band-cards are less relevant, but I use Lightshow to save a couple of minutes of each game, and Flurry (Rank 1) for surviving to that point, and also getting another risk-free spell for the quest. You get these by using Potion of Illusion or Youthful Brewmaster on your E.T.C., Band Manager.

When I say a risk-free spell, I mean a generated spell that can be played and has no risk of backfiring, by either killing you or messing up your combo, when replayed by Grand Magister Rommath. So it can not include card-draw, except perhaps some targeted card-draw, like Ancient Mysteries which loses its effect later in the game. The same goes for spells that generate other spells, as they clog your hand. You also don't want spells that summon minions, outside cloning existing friendly minions, like Molten Reflection, as you would clog your hand with Potion of Illusion replayed.

In general, playing non-risk-free spells is an unnecessary risk, and therefore you don't even want to risk generating them, if you have better options, as they clog your hand. Minion summoning spells could be almost risk-free if you use Simulacrum instead of Potion of Illusion, and play a very minion-thin deck, in order to avoid drawing minions on your combo turns.

Plan your turns ahead, think of what it is you need, and don't waste time, as there are a few cards in wild that can mess up your combo, like a lot of the "swap" cards, cards that destroy cards in your hand or deck, as well as cards that play around Ice Block. I will now explain card choices:

Evocation is an incredible tool in this deck, as you only want to play a few of the generated spells, you are more than happy to let the other ones be discarded.

Open the Waygate can actually be replaced in some metas, by instead winning with the damage of Lightshow through 1-cost Grand Magister Rommaths. Otherwise, Time Warp can be played whenever to get a lot of time.

Sphere of Sapience works like a selective card draw, where you get what you need and abstain from clogging your hand. Among my favorite cards in the whole game.

Violet Spellwing is an appropriate card, it can give you a bit of time in faster matchups and the Arcane Missiles makes for faster games when you finish. Small minions and cards like this can also be very good to play around Secrets and Blademaster Okani.

Ancient Mysteries is very replaceable, but makes you go through the deck at a low cost, and can give you some time in matchups where you can rely on that the enemy won't sabotage your combo or play around Ice Block.

Conjure Mana Biscuit is very good, getting more mana can speed up your tempo and game achievements. I often try to save one Mana Biscuit or The Coin to play E.T.C., Band Manager, and Potion of Illusion or Youthful Brewmaster in the same turn prior to turn 8.

Licensed Adventurer is quite appropriate and high tempo, especially in faster matchups.

Questing Explorer is good for similar reasons, not too exciting but not easily replaced.

Research Project is very meta-dependent and could very well be replaced, but I often like the sheer speed of it.

Rewind is an amazing card for this deck, keep track of what spells you've played to maximize its value. I generally try to get Ice Block, Frost Nova, or Mana Biscuit. Conjure Mana Biscuit can be a low-risk Spell to generate in fast matchups, and greatly help you finish your Quest.

Sketchy Stranger is almost always very good, but a risky aspect, as you might not be much of a fan of those Secrets you get. However, there sure are cards I'd replace before this one.

Youthful Brewmaster has a variety of uses, as the deck has 8 other relevant Battlecries to repeat, depending on what you need in the match. It's certainly very low-tempo, but the flexibility should not be underestimated. In some metas, Zola the Gorgon would be a better fit.

Frost Nova is generally needed in most matchups.

Ice Barrier is often a pretty good target for a lot of cards in your deck and can give you time in a lot of matchups.

Ice Block is a very reliable card that shows great use in this deck. When you choose to rely on it in a match, you could aim to generate a few with Rewind and Volume Up, doing so with the earlier becomes a lot easier with Ancient Mysteries, but a lot harder with the latter. Also, if it fails to prove reliant, you have wasted resources on generating it.

E.T.C., Band Manager is crucial for the combo due to the interaction with Potion of Illusion in his Band, and Grand Magister Rommath. However, you can at times win without him, especially with Youthful Brewmaster.

Lorekeeper Polkelt can immensely increase the consistency of the deck, when you wish to play him depends mainly on how far you've progressed on your quest, or have the ability to do with your hand. Some metas and deck variations could prove it more advantageous to replace him with Taelan Fordring. Playing with neither I believe is too hand-clogging, and slow.

Volume Up is extremely high value in this deck, and generating Ice Block with it becomes very reliant after you've played Lorekeeper Polkelt. However, due to him, I only play one copy of this currently, to not delay drawing E.T.C., Band Manager more than necessary.

Grand Magister Rommath is the least replaceable card in the deck, losing it almost always costs you the game.

Deck variations:

Skipping Open the Waygate, for a faster deck that can OTK, but does not need to in order to win.

Replacing E.T.C., Band Manager with finite ways to copy Grand Magister Rommath, and taking the chance to get infinite, by copying Potion of Illusion and Echo of Medivh.

Replacing Ice Barrier with Mana Giant, Arcane Giant, or Naga Giant to utilize cheap tempo and maybe force defensive measures.