Preheat oven to 400°F with racks in upper and lower thirds.

Line 2 baking sheets with parchment paper.

Whisk flour and pepper in a medium bowl.

Combine 1½ cups water, butter, and kosher salt in a large saucepan;

Cook over medium-high, stirring occasionally, until mixture just comes to a boil.

Add flour mixture to saucepan all at once.

Stir quickly using a wooden spoon until a smooth dough forms and dough pulls away from sides of pan, 2 to 3 minutes.

Remove from heat.

Add cheese and stir until mostly melted and smooth, about 1 minute.

Add eggs 1 at a time, stirring vigorously after each addition, until smooth. (Batter will appear lumpy after each egg but will smooth out as you stir.)

Transfer dough to a large zip-top bag with a ½-inch tip of 1 corner cut off (or a pastry bag fitted with a ½-inch round tip).

Pipe 1 ½-inch mounds, spaced at least 1 inch apart, onto prepared baking sheets (about 24 per baking sheet).

Flatten any pointy tips with your fingertip.

Top with flaky sea salt and more pepper. Transfer any remaining batter in bag to refrigerator.

Bake until puffed and golden, 30 to 35 minutes.

Let cool for 5 minutes.

Repeat with any remaining dough, reusing parchment paper on slightly cooled baking sheet.

Keep warm in a 200°F oven.

Cheese puffs can be made up to 3 hours ahead;

Reheat in a 225°F oven on a baking sheet lined with parchment paper until hot, about 15 minutes.