1. In a 3- to 4-quart pan over high heat, bring 1 1/2 cups water and the butter to a full rolling boil. Remove from heat, add flour all at once, and stir until mixture is a smooth, thick paste with no lumps. Add a quarter of the beaten eggs at a time, stirring vigorously after each addition until dough is no longer slippery. Stir in cheese and pepper.
2. Spoon dough into a large pastry bag fitted with a plain 1/2-inch round tip. Pipe in 48 equal mounds on two cooking parchment-lined or buttered 12- by 15-inch baking sheets. (Alternatively, drop dough on sheets in slightly rounded tablespoon-size portions.) Sprinkle each mound with a few grains of coarse sea salt.
3. Bake in a 400° regular or convection oven until dry and well browned, about 30 minutes. Serve warm (see notes).
Nutritional analysis per puff.
These easy puffs are especially good made with strongly flavored, aged white English, Irish, or Canadian cheddar. We like to use an imported sea salt with pretty, crunchy crystals, such as fleur de sel, Halen Môn, or Maldon, but any coarse sea salt will work. The puffs can be made up to 1 month ahead and frozen; cool, then freeze airtight. Reheat thawed puffs, uncovered, in a 375° oven until crisp and hot, about 5 minutes.