Preheat oven to 425°F. Line a baking sheet with parchment paper.
In a heavy bottom pan bring water, butter, salt, pepper and nutmeg to a boil. When butter is melted and water is boiling, remove from heat.
Stir in flour and cook over medium high heat for 1-2 minutes. The dough should leave the side of the pan clean and a slight film on the bottom. Remove from heat.
Make a well in the center of the dough and add one egg. Beat in egg until incorporated. Repeat with three more eggs, stirring each one in completely before adding the next.
Stir the cheese into the warm dough.
Place dough in a pastry bag or use a soup spoon to make 1 inch diameter and 1 inch high mounds (optional: for a true Julia Child touch, make a small peak on the top of the mound).
In a small bowl combine remaining egg and ½ teaspoon of water. Brush the egg mixture on top and sides of the puffs without letting it drip all the way to the parchment paper. This will prevent the puffs from rising.
Bake about 20 minutes until golden brown. Remove from oven and turn the oven off. Pierce each puff with a knife to release steam and return to the turned off oven for 10 minutes to dry out.