Preheat the oven to 400℉. Line a rimmed baking sheet with a silicone baking mat or a buttered sheet of parchment paper.
In a large stainless-steel saucepan over medium-high heat, combine the butter, water, milk, salt and nutmeg. Bring to a rapid boil, stirring to combine as the butter melts. Reduce the heat to medium and, using a wooden spoon, stir in the flour all at once. Cook, stirring constantly, until the dough dries out slightly, about 1 minute. This is important- excess moisture will cause your puffs to collapse. Remove the pan from the heat and let the dough cool for 5 minutes.
Stir in the eggs, one at a time, until fully incorporated before adding the next. You can mix in the eggs with a mixer, food processor or a wooden spoon. Beat in all but 2 tablespoons of the Gruyere.
Place the dough in a pastry bag fitted with a ½-inch plain tip and pipe golf ball-size puffs onto the prepared baking sheet.
In a small bowl, whisk together the egg yolk and water. Brush the tops of the puffs lightly with the egg wash, sprinkle with the remaining 2 tablespoons of Gruyere, and bake for 20 minutes.
Reduce the oven temperature to 350℉ and continue baking until golden brown and dry, about 20 minutes. Cool on a wire rack. Eat warm or serve later. They will keep at room temperature for a few hours. Reheat in a 375℉ oven for 5 minutes before serving.