3 cups whole milk
3/4 cup semolina (sometimes labeled "semolina flour"; resembles fine yellow cornmeal)
1 teaspoon salt
1/4 cup plus 2 tablespoons unsalted butter, melted
3 oz finely grated Parmigiano-Reggiano (3/4 cup)
1 large egg
Whisk together milk, semolina, and 1 teaspoon salt in a 2-quart heavy saucepan and bring to a boil over moderate heat, whisking. Simmer, stirring constantly with a wooden spoon, until very stiff, 5 to 8 minutes. Remove from heat and stir in 2 tablespoons butter and 3/4 cup Parmigiano-Reggiano. Beat in egg.
Spread gnocchi mixture 1/2 inch thick on an oiled baking sheet and chill, uncovered, until very firm, about 1 hour.
Preheat oven to 425°F.
Cut out rounds from gnocchi mixture with a 2-inch round cookie cutter (push scraps into remaining mixture as you go) and arrange, slightly overlapping, in a well-buttered 13- by 9-inch baking dish. Make a small second layer in center of dish with any remaining rounds. Brush gnocchi with remaining 1/4 cup melted butter and sprinkle with remaining 3/4 cup Parmigiano-Reggiano.Bake in middle of oven until gnocchi are beginning to brown, 15 to 20 minutes. Let stand 5 minutes before serving.
Makes 6 first-course servings.