Gnocchi alla Romana

INGREDIENTS

• 5 1/2 cups milk
• 2 cups semolina
• 2 tsp. kosher salt
• 1 1/4 cups grated Parmigiano-Reggiano cheese
• 2 egg yolks
• 6 Tbs. (3/4 stick) unsalted butter, cut into small cubes, plus 3 Tbs. melted butter
• Roman-style meatballs for serving (see related recipe at left)