Chef John's Party Cheese Puffs

Preheat oven to 425 degrees F (220 degrees C). Line a baking sheet with a silicone baking mat.

Stir water, butter, and salt together in a pot; bring to a simmer. Reduce heat to medium and whisk flour into butter mixture until a paste-like dough forms, 2 to 3 minutes. Transfer dough to a bowl to cool until warm, 5 to 10 minutes.

Whisk 1 egg, thyme, and black pepper into cooled dough until egg is completely incorporated. Add remaining egg and whisk until completely incorporated into dough. Stir 3/4 the cheese into dough until combined. Scoop 1-inch balls of dough onto prepared baking sheet. Top each with remaining cheese.