Step 1

Position a rack in the middle of the oven and preheat to 400 degrees. Use a little butter to grease a 9-by-13-inch baking dish.

Step 2

In a medium saucepan over medium-high heat, combine the milk and salt. Stirring and scraping the bottom of the pot with a rubber spatula to prevent scorching, bring to a simmer and reduce the heat to medium-low to prevent a boil-over. Then sprinkle in the semolina, stirring constantly as you do. Cook, stirring, until the mixture is so thick that the spatula can stand in the middle without falling over, 2 to 3 minutes.

Step 3

Let cool for a few minutes, then add half of the butter (4 tablespoons) and 1/2 cup of the cheese, stirring until the butter and cheese melt and the mixture is thoroughly combined. Add the egg yolks, one at a time, and stir until incorporated. The mixture should be the texture of thick mashed potatoes.

Step 4

Scrape the semolina mixture onto a large sheet pan and use wet hands, a damp knife or offset spatula to spread it out evenly, and pat the top to smooth it. (It should be about 1/2 inch thick, but it’s okay if it’s a little thicker.) Let cool to room temperature, about 5 minutes.

Step 5

Fill a small bowl with water. Dip a two-inch cookie cutter, biscuit cutter or drinking glass in the water and use it to stamp out rounds, re-dipping frequently, or use a knife to cut it into two-inch squares. If cutting into rounds, mush together and spread out the scraps again and keep cutting, repeating until all of the mixture is used.

Step 6

Arrange the pieces in overlapping rows, like shingles, in the buttered 9-by-13-inch dish. Sprinkle them with the remaining 1 cup of the pecorino, and top with the remaining pieces of butter.

Step 7

Bake for 15 to 20 minutes, or until the cheese is browned in spots. Grind a generous amount of pepper on top and serve warm.