Butter a 13" x 9" baking dish.
Heat milk in a medium saucepan.
When milk begins to boil, reduce heat and add semolina very slowly, whisking quickly to avoid lumps.
Cook 10 to 15 minutes over medium-low heat, stirring constantly with whisk.
Semolina is cooked when it sticks heavily to whisk.
Remove pan from heat.
Add 3 tablespoons butter, 1/3 cup Parmesan cheese, egg yolks and salt.
Mix quickly until well blended.
Moisten a work surface or a large dish with water.
Pour semolina mixture onto surface and spread it 1/2 inch thick with a wet spatula.
Let it cool.
Preheat oven to 400F (205C).
With a small glass or cookie cutter, cut cooled semolina mixture into 2-inch rounds.
Arrange in buttered baking dish, overlapping rounds slightly.
Dot with about 1 tablespoon butter and sprinkle with remaining Parmesan cheese.
The dish can be prepared to this point and refrigerated a couple of days.
Bake 10 to 15 minutes or until golden.
For a golden-brown crust, put briefly under preheated broiler.