Preheat oven to 400°F. Butter 2 large baking sheets.
Bring 1 cup water, butter, salt and pepper to a boil over medium-high heat. Add flour; beat with a wooden spoon until mixture forms a ball.
Transfer dough to a large bowl. With electric mixer on high speed, add eggs 1 at a time, beating well after each. Beat until mixture is smooth and has cooled. Beat in cheese.
Drop spoonfuls of mixture 1 inch apart on baking sheets. With dampened fingers, smooth tops. Bake until puffed and golden, 25 to 30 minutes. Cool on pans on wire racks. Slice off top third; discard doughy centers. Fill, if desired, and replace tops.