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.
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.
Bake in a 400° regular or convection oven until dry and well browned, about 30 minutes. Serve warm (see notes).
Nutritional analysis per puff.