Step 1

Rub a 1-tablespoon piece of butter over a rimmed baking sheet (approximately 13-by-18 inches) and a 9-by-13 inch baking dish; set aside.

Step 2

In a large saucepan over medium, heat the milk to just below a simmer. While whisking constantly, slowly stream in the semolina. Switch to a silicone spatula or wooden spoon and cook, stirring often, until the mixture is thick, slightly elastic and pulls away from the sides of the pan, 6 to 8 minutes.

Step 3

Off heat, add the remaining 5 tablespoon-size pieces of butter, half of the Parmesan, the nutmeg and 1¼ teaspoons each salt and pepper; stir until the butter is melted and incorporated. Add the eggs, then stir vigorously until well combined.

Step 4

Pour the mixture into the center of the prepared baking sheet and, using a spatula, spread into an even layer all the way to the edges. Refrigerate, uncovered, until fully chilled, about 1 hour; for longer storage, once chilled, cover with plastic wrap and refrigerate up to 24 hours.

Step 5

About 20 minutes before you plan to bake, heat the oven to 425°F with a rack in the upper-middle position.

Step 6

Remove the baking sheet from the refrigerator. Using a dinner knife, cut the semolina slab into quarters lengthwise and sixths crosswise to make 24 rough squares. Remove the pieces from the baking sheet (a thin metal spatula works well) and arrange them in the prepared baking dish, shingling them to fit. Brush the melted butter onto the gnocchi, then sprinkle with remaining Parmesan.

Step 7

Bake until the cheese is melted and the gnocchi are browned in spots, 30 to 35 minutes. Cool for about 10 minutes before serving.