Preheat oven to 425 degrees F. Butter one cookie sheet with 3/4 inch sides.
In a 3 to 4 quart saucepan, heat to scald milk, salt and 6 tablespoons butter. Pour in polenta in a thin stream, whisking vigorously, and cook for about a minute, switching to a wooden spoon as polenta thickens. Remove from heat and stir in 1/2 cup grated cheese and 4 egg yolks and mix well. Pour polenta in buttered cookie sheet and 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 the polenta. Arrange leaning up against one another in a buttered baking dish and sprinkle with remaining grated cheese. Place in oven and cook 15 to 20 minutes, or until top is light golden brown. Remove and serve immediately.