Cheese Puffs (Gougères)

Name: Cheese Puffs (Gougères)
Prep time: 20 min
Cook time: 40 min
Total time: 1 h
Yield: 24 puffs
Ingredients: Ingredients; 1 cup water; 8 tablespoons (1 stick) unsalted butter, cut into pieces; 1 teaspoon salt; 1 cup all-purpose flour; 4 large eggs, room temperature; 1 cup Gruyère cheese, finely grated (divided); 1/2 cup Parmesan cheese, finely grated; 1/4 teaspoon freshly ground black pepper; 1/4 teaspoon cayenne pepper (optional); 1/8 teaspoon nutmeg, freshly grated; 1 egg, beaten (for egg wash)