Preheat the oven to 425°F.
Boil the water in a 2-quart saucepan with the 6 tablespoons butter and the salt. Remove from the heat and beat in the flour all at once with a wooden spoon. Beat the mixture vigorously until the paste is smooth and pulls away from the pan, or “rounds itself.” Add a few grinds of the white pepper.
Either by hand or in a mixer, beat in the eggs one at a time until fully incorporated. Then mix in the cheese. Stop beating when the batter is stiff.
Butter a baking sheet and put the paste into a pastry bag fitted with a ¾-inch round tube tip. Squeeze the paste onto the baking sheets in mounds 2½ inches in diameter and 1 inch high in the center. Alternatively, the paste can be dropped from a spoon, but the shapes will not be as neat. Make sure the mounds are at least 2 inches apart.
Bake for 5 minutes. Reduce the oven temperature to 350°F and cook for another 20 minutes. Set the puffs on the door of the turned-off oven for 15 minutes to dry out. Cut off the very top of the puffs and scoop out any damp interior pastry. (The tops are for snacks.)