Gnocchi alla Romana

4 cups milk
1 1/2 cups semolina (about 8 oz.)
1 1/2 cups finely grated Parmesan
8 tbsp. unsalted butter, softened
2 egg yolks, beaten
Kosher salt, to taste

In a 5-qt. pot over medium-high heat, bring milk to a simmer while stirring. Reduce heat to low; slowly whisk in semolina. Cook, whisking, until tender, 8?10 minutes. Whisk in 1/2 cup Parmesan, 4 tbsp. butter, and yolks; season with salt. Remove from heat.

Wet a 15? x 10? rimmed baking sheet with a soaked paper towel. Pour semolina mixture onto baking sheet; smooth surface with spatula to 1?2? thickness. Let cool until firm, about 40 minutes.

Heat oven to 450. Using a knife, cut gnocchi dough in 2? squares; transfer half of the squares to a buttered 9? x 13? baking pan. Sprinkle gnocchi with 1?4 cup Parmesan and dot with 2 tbsp. butter. Layer remaining gnocchi on top and sprinkle with 1/4 cup cheese and remaining butter. Bake until golden, about 15 minutes. Serve with remaining cheese.
Serve with Finocchio con Latte al Forno