Preheat the oven to 425 degrees F.
Butter 1 cookie sheet with 3/4-inch sides and a baking dish.
In a 3 to 4-quart saucepan, heat to scald the milk, salt, and 6 tablespoons butter. Pour in the semolina in a thin stream, whisking vigorously, and cook for about 1 minute, switching to a wooden spoon as it thickens. Remove from the heat and stir in 1/2 cup grated cheese and 4 egg yolks. Mix well to combine. Pour the semolina onto the buttered cookie sheet and, using a spatula, spread to a thickness of 1/2-inch. Allow to cool.
Using a pastry cutter or water glass, cut 3-inch quarter moons out of semolina. Arrange the moons so that they are leaning up against one another (overlapping) in a buttered baking dish and sprinkle with remaining grated cheese. Place in oven and cook 15 to 20 minutes, or until top is deep golden brown. Remove and serve immediately.