Roman Semolina Gnocchi

Ingredients

• 6 cups milk
• Kosher salt
• 1 1/2 cups semolina flour
• 8 tablespoons unsalted butter, divided, plus more for greasing
• 1 cup grated Parmigiano-Reggiano, plus more for grating
• 3 egg yolks, lightly beaten

Directions

1. Warm the milk in a large saucepan over medium-high heat, whisking now and then so it does not catch on the bottom, until it is steaming. Add a good amount of salt. Whisk continuously as you add the semolina in a thin, steady stream, which helps keep the mixture smooth; it will tighten up and become harder to whisk. When all the semolina is in, reduce the heat to medium-low, trade the whisk for a sturdy rubber spatula or wooden spoon, and continue cooking, stirring the whole time, until the mixture turns into a sticky dough that starts coming away from the sides of the pan, 10 to 15 minutes. Be sure to work the utensil into the corners and across the bottom so nothing scorches. Take the pan off the heat.
2. Add 4 tablespoons of butter and stir until it has melted completely into the dough. Stir in the cheese until it is melted and fully mixed in. Add the egg yolks and keep stirring until they are evenly incorporated.
3. Transfer the semolina dough to a buttered rimmed baking sheet. With a damp rubber spatula or clean damp hands, wetting them again as needed to keep the dough from sticking, pat and smooth it into an even layer about 1/2 inch thick. The dough does not need to cover the entire pan, as long as the thickness is consistent. Lay plastic wrap directly on the surface and chill until firm, at least 40 minutes and up to overnight.
4. Heat the oven to 450 degrees F. Cut the chilled semolina into rounds with a 3-inch round cookie cutter or a glass of a similar size. The scraps can be kept in the refrigerator for up to 4 days and deep-fried for a snack, or layered in a smaller baking dish for a mini version. Butter a large baking dish or an ovenproof skillet. Slide a thin metal spatula under each round to lift it from the baking sheet, then shingle the rounds in the prepared dish or skillet.
5. Melt the remaining 4 tablespoons butter and spoon or pour it over the semolina gnocchi. Grate a generous layer of Parmigiano-Reggiano over the top. Bake until the gnocchi are hot and bubbling with browned tops, about 15 minutes. Serve with more grated cheese to pass at the table.