How to Make It
Preheat the oven to 400°. Lightly butter 2 large baking sheets. In a large saucepan, combine the milk with the water, butter, sugar, salt, cayenne and nutmeg and bring to a boil. Remove the pan from the heat, add the flour and stir with a wooden spoon until a thick, smooth pastelike batter forms. Cook the batter over moderate heat for 1 minute, stirring constantly.
Scrape the batter into a large heatproof bowl and add 4 of the eggs, beating them in 1 at a time until fully incorporated. Beat in 11/4 cups of the cheese.
Using a pastry bag fitted with a 1/2-inch plain round tip or 2 small spoons, pipe or spoon slightly rounded tablespoons of the batter onto the prepared baking sheets, spacing them 1 inch apart. Lightly beat the remaining egg. Brush the tops of the gougères with the egg wash, then sprinkle them with the remaining 1/2 cup of shredded cheese. Bake the gougères for 20 minutes, or until puffed and golden; shift the pans from front to back and top to bottom halfway through. Serve warm.