Position 1 rack in top third and 1 rack in bottom third of oven; preheat to 400°F Line 2 rimmed baking sheets with parchment paper.
Bring 1 cup water, buter, and salt to simmer in heavy medium saucepan over medium heat, whisking until butter melts. Add flour; stir rapidly with wooden spoon until flour absorbs liquid and forms ball, pulling away from sides of pan. Stir vigorously until film forms on bottom of pan and dough is no longer sticky, 1 to 2 minutes longer. Remove pan from heat; cool dough 2 to 3 minutes. Using electric mixer, beat in eggs, 1 at a time. Stir in cheese and pepper.
Drop rounded tablespoonfuls of dough onto baking sheets, spacing about 3 inches apart. Using damp fingertip, press down any peaks of dough.
Bake gougeres until golden brown, about 30 minutes, reversing position of pans halfway through baking. Using small sharp knife, pry open 1 gougere to check doneness (center should be slightly eggy and moist). Serve hot or warm.
*Can be made 3 hours ahead. Transfer to racks; cool. Rewarm in 350 F oven for 5 to 10 minutes.