Preheat oven to 425°. In a medium saucepan over medium-high heat, bring 1 cup water to a low simmer. Add butter, salt, and nutmeg; cook, stirring, until butter melts. Remove from heat, add flour, and stir well to remove any lumps. Return to heat. Cook, stirring vigorously, until dough pulls cleanly from sides of pan and forms a smooth ball, 1 to 2 minutes.
Transfer dough to bowl of a stand mixer fitted with the paddle attachment. One at a time, add 4 eggs, beating on medium speed until each is absorbed before adding the next. Blend in cheese and olives.
Drop 1-tbsp. portions of dough 1 1/2 in. apart onto two greased baking sheets to make 44 total. Whisk remaining egg to blend and brush a little over dough.
Bake cheese puffs 20 minutes, switching pan positions halfway through. Reduce oven to 375° and bake until deep golden brown and crisp, 5 more minutes. Loosen from pan and serve immediately.
Make ahead: The baked puffs, up to 1 month, frozen airtight; reheat frozen on baking sheets in a 375° oven until hot, about 5 minutes.