Step 1: Preheat your oven to 400°F (200°C) and line two baking sheets with parchment paper or silicone mats.
Step 2: In a medium saucepan, combine the butter, water, salt, and pepper. Bring the mixture to a rolling boil over medium-high heat, stirring until the butter is completely melted.
Step 3: Remove the saucepan from the heat and immediately add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a ball and pulls away from the sides of the pan. Return the pan to medium heat and cook, stirring constantly, for 1-2 minutes to dry out the dough. You'll see a slight film on the bottom of the pan.
Step 4: Transfer the dough to a large mixing bowl (or a stand mixer with a paddle attachment). Let it cool for 5 minutes, stirring occasionally, to prevent the eggs from scrambling when added.
Step 5: Add the eggs one at a time, mixing thoroughly after each addition until fully incorporated. The dough may look curdled at first, but keep mixing until it comes together smoothly. The final dough should be smooth, glossy, and fall slowly from a spoon in a 'V' shape.
Step 6: Stir in the grated cheddar cheese until just combined.
Step 7: Transfer the dough to a piping bag fitted with a large round or star tip (or use two spoons). Pipe 1-inch mounds onto the prepared baking sheets, leaving about 1-2 inches between each puff.
Step 8: Bake for 15 minutes at 400°F (200°C). Then, reduce the oven temperature to 350°F (175°C) and continue baking for another 10-15 minutes, or until the puffs are deeply golden brown, puffed, and firm to the touch. Do not open the oven door during the first 20 minutes of baking.
Step 9: Turn off the oven, crack the door slightly, and let the cheese puffs sit in the oven for an additional 5-10 minutes. This helps them dry out further and prevents deflating. Serve warm and enjoy!