Gnocchi alla Romana (Baked Semolina Cheese Rounds)

Semolina is cooked in milk, cooled in an even 1.5 cm sheet, cut into rounds, and baked under butter and cheese. Combine 500 ml milk, 1 teaspoon salt, 1/4 teaspoon nutmeg, and 20 g butter in a saucepan. Heat over medium until steam rises and the edges begin to tremble, without bringing the milk to a hard boil. Lower the heat and pour in 150 g semolina in a thin, steady stream while whisking continuously for 1 minute. Reach into the bottom and corners so no dry pockets harden into lumps. Switch to a sturdy spatula and continue stirring over low heat for 4 to 5 minutes. Turn off the heat when the mixture pulls cleanly from the sides and gathers into a thick, smooth mass. While it remains hot, quickly mix in 2 egg yolks and part of the 80 g Parmigiano Reggiano. Continuous mixing prevents the residual heat from scrambling the yolks into separate pieces. Spread the dough across a tray at a uniform 1.5 cm thickness and smooth the top. Let it cool completely until firm; cutting while warm tears the sheet and leaves rough edges. Stamp out rounds and overlap them in a buttered baking dish. Distribute the remaining 20 g butter and Parmigiano over the surface. Bake at 200C for 15 minutes, then broil for about 3 minutes, stopping when the raised edges and cheese are golden and crisp.