Found exclusively by killing Stag Beetles, Hearts of the Stag are a powerful, high-tier food, both cooked and raw. Raw hearts restore 20 health (10 full hearts!), making them invaluable in a situation where normal health regen just won't cut it. Raw hearts can be eaten anytime, full hunger or not.
Cooked Hearts of the Stag work similarly. Instead of restoring 20 health, they restore 20 hunger points (10 full hunger icons!) and max out your hunger saturation. This is balanced by the fact that Hearts of the Stag are a rare drop from Stag Beetles, rather than a guaranteed drop like Titan Chops.
Hearts of the Stag, both cooked and raw, continue beating whilst in the player's inventory or in a Chest.