5 1/2 cups milk
2 cups semolina flour
2 tsp. kosher salt
1 1/4 cups Parmigiano-Reggiano cheese, grated
2 egg yolks
6 Tbs. (3/4 stick) unsalted butter, cut into small cubes, plus 3 Tbs. melted butter
In a 4-quart saucepan over medium-high heat, bring the milk to a simmer. Add the semolina in a slow, steady stream, whisking constantly until incorporated. Reduce the heat to medium-low, add the salt and continue whisking to prevent lumps from forming. Cook, stirring and scraping the bottom and sides of the pan, until the semolina is thick and starts to pull away from the sides of the pan, about 10 minutes. Remove from the heat and stir in 3/4 cup of the cheese, the egg yolks and the 6 Tbs. (3/4 stick) butter until incorporated.
Spray a 9-by-13-inch pan with nonstick cooking spray, line the bottom with parchment paper and spray again. Pour the semolina mixture into the pan, spreading it evenly and smoothing the top with a rubber spatula. Cover and refrigerate until firm, about 2 hours.
Preheat an oven to 425°F. Butter a 9-inch skillet.
Using a 2 1/2-inch cookie or biscuit cutter, cut the gnocchi into rounds. Arrange the gnocchi in the pan so they are overlapping, resembling shingles. Brush the top of the gnocchi with the 3 Tbs. melted butter and sprinkle with the remaining 1/2 cup cheese. Transfer the pan to the oven and bake until the top is golden brown, 30 to 35 minutes. Let rest for 10 minutes, then serve immediately with Roman-style meatballs. Serves 6 to 8.