Update - Priest Rework

With the Priest rework in March 2020, Power Word: Shield and Shadow Word: Death (from the original list) no longer fit the odd mechanic requirements of Baku the Mooneater. As such, I removed them and replaced them with Dark Prophecy and Tar Creeper. I'm not sure they are the best fits, but wants high health minions, so I thought these would fit.

Deck Idea

The goal of this deck is to get high health minions to stick on board while completing Activate the Obelisk. Once we complete the quest, our new hero power, Obelisk's Eye, makes our minions even stickier, allowing us to finish the game with the Glitter Moth+Inner Fire combo.

Mulligan

Against Aggro

Fortunately, Priest's odd hero power, Heal, from Baku the Mooneater is a great anti-aggro tool in the early game. Combined with high health minions early game, we can make good trades to counter the opponent's board presence; Extra Arms makes it even easier for our early game minions to make favorable trades. Additionally, Stonehill Defender is a great tool to fill out our curve with a taunt minion to slow our opponent down. If these cards don't cut it, keeping a Mass Hysteria can stop most rush-down by turn 5.

Against Control

When playing against slower decks, our main focus should be setting up our finishing combo: Glitter Moth+Inner Fire. The best way to set up early game is to develop high health minions. Generally, we want to mulligan for all of the same cards as against aggro; however, instead of Stonehill Defender, we want to get Banana Buffoon. Banana Buffoon allows us to buff our early game minions or combo with Recurring Villain on turn 6.

Tips

Playing Activate the Obelisk on turn 1 is not critical with this deck since all of our healing comes form our Heal. In general, playing Crystallizer or Northshire Cleric on turn 1 is more valuable than playing Activate the Obelisk. Unless I don't have any cards to play, I usually don't play Activate the Obelisk until I am actually going to heal myself or a minion. Sometimes, this means I don't play Activate the Obelisk until turn 4 or 5.

Since this deck's main goal is to pull off the classic Divine Spirit+Inner Fire combo (using Glitter Moth+Inner Fire), your main goal should be to get your minions to stick on board. Fortunately, this deck runs a lot of high health minions that aren't the easiest to remove. Both of the hero powers we have access to help us keep their health high so we can pull of our finishing combo. Also remember that Glitter Moth doubles the health of all of our minions (unlike Divine Spirit), so Glitter Moth can be a huge tempo play if we have a lot of minions on board--it might not set up lethal that turn, but it can make a board full of high health minions that are ridiculously difficult to remove.

Recurring Villain is one of the strongest cards in the deck because of the synergy it has with Banana Buffoon, Extra Arms, and Obelisk's Eye. On turn 6, we can play Recurring Villain+Bananas to create a 4/7 that summons a 3/6. If we have Obelisk's Eye ready or an Extra Arms, we can keep Recurring Villain alive for many turns until we finally get the Glitter Moth+Inner Fire combo.

In the late game, the most important thing to focus on is the health of our minions and how to maximize our damage using Glitter Moth+Inner Fire. Since Glitter Moth+Inner Fire is 6 mana, we don't have the luxury of a ton of extra mana to super buff our minions in a single turn; thus, utilizing Obelisk's Eye and holding on to Bananas for the late game can be the difference between lethal and 2 health remaining on the enemy hero.

Good luck, and have fun! This deck is a lot of fun if you like using uncommon cards (such as Recurring Villain or Glitter Moth).