Preheat & Prepare: Preheat your oven to 425°F (220°C) and line two large baking sheets with parchment paper.

Cook the Dough: In a medium saucepan, combine the milk (or water), butter, salt, and cayenne pepper. Bring to a boil over medium heat. Once boiling, reduce the heat and stir in the flour all at once. Continue to cook and stir until the dough is smooth and no longer sticky, about 2-3 minutes. Remove from heat and let cool for 5 minutes.

Incorporate Eggs and Cheese: While the dough is cooling, whisk the eggs in a separate bowl. Remove 2 tablespoons of the eggs and set aside for an egg wash. Gradually stir the rest of the eggs into the dough, adding a little at a time and stirring well after each addition. Once the eggs are fully incorporated, stir in the shredded cheese.

Shape the Puffs: Transfer the dough into a piping bag or a freezer bag with the tip cut off. Pipe 1-inch circles (about ¾ inch high) onto the prepared baking sheets. Use wet fingers to smooth the tops of the mounds.

Bake: Brush the puffs with the reserved egg wash. Bake for 25-30 minutes, or until the cheese puffs are golden brown and puffed up. Serve warm.