Preheat oven to 425°F. Line a baking sheet (or two) with parchment paper.

Make the egg wash by lightly beat one egg with 1/2 teaspoon water. Set aside.

In a medium saucepan, combine water, butter, salt, white pepper, and nutmeg and bring to a boil. When butter melts, reduce heat to low. Add flour to saucepan and continue cooking over low heat while stirring with a wooden spoon. Stir for about 1 minute. When the mixture pulls away from the sides of the saucepan (may be less than a minute), remove it from heat. Add the cheese to the saucepan; stir vigorously until it is mixed in well. Next, add the remaining four eggs, one at a time, beating each egg into the mixture with the wooden spoon. Continue beating until batter is shiny and smooth.

Form each gougère by dropping batter, in heaping teaspoon size, onto the cookie sheet(s). Use a soup spoon to make larger gougères.

Brush tops of gougères with the egg wash. Bake in top part of oven for 15-20 minutes until deep golden and doubled in size.

Serve hot or room temperature. They will deflate as they cool, but they will still taste great.