How to Make It
In a small saucepan, combine the water, salt and nutmeg with 2 tablespoons of the butter and bring to a boil over high heat. As soon as the water boils, add the flour all at once and beat the dough with a wooden spoon until it is thick and comes away from the side of the pan. Cook, stirring to dry out the dough, about 30 seconds. Transfer the dough to a medium bowl and let cool slightly, about 5 minutes.
Beat 1 egg into the dough until incorporated. Beat in 1/4 cup of the cheese and another egg until blended, then beat in the last egg until the dough is very smooth.
Preheat the oven to 350°. Bring a large pot of salted water to a boil. Set a bowl of ice water near the stove. With a large spatula, transfer the dough to a resealable plastic bag, pressing it into one corner. Cut off the tip of the bag; the opening should be about 1/2 inch long.
Reduce the heat to maintain a gentle simmer. Carefully hold the bag over the water and press out the dough, using a small sharp knife to cut it into 1 1/2-inch lengths before it drops into the pot (see Note). Simmer the gnocchi for 3 minutes. With a slotted spoon, transfer the gnocchi to the ice water bath to stop the cooking. Transfer the gnocchi to paper towels and pat dry.
Grease a 9-by-12-inch baking dish with the remaining 1 tablespoon of butter. Arrange the gnocchi in the dish and sprinkle with the remaining 2 tablespoons of cheese. Bake until puffed, about 25 minutes. Preheat the broiler. Broil the gnocchi 6 inches from the heat for 1 to 2 minutes, or until browned. Serve right away.
The gnocchi dough can also be shaped with 2 teaspoons.