preheat 425 degrees.
Add butter, salt, pepper and nutmeg to 1 cup water in medium saucepan and bring to a boil over medium-high heat. When butter melts, reduce heat to low.
Add flour to butter-water mixture all at once and cook over low heat, beating with a wooden spoon, for 1 minute, until mixture pulls away from sides of pan. Remove pan from heat. Add cheese to pan and beat in with a wooden spoon until well incorporated. Add 4 of the eggs, 1 at a time, beating each egg into the batter unil thoroughly absorbed. Continue beating mixture until it is smooth, shiny, and firm.
Drop batter in small spoonfuls onto a lightly greased cookie sheet to form Gougeres. Beat remaining egg with 1/2 tbsp water, then brush tops of uncooked Gougeres with egg wash.
Bake in upper third of oven for 15-20 minutes or until Gougeres are golden and doubled in size. Remove from oven and serve hot, or allow to cool to room temperature.
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