Melt butter in a heavy saucepan. Add flour; stir until thick and bubbly. Add milk, salt, and pepper; keep stirring. Remove from heat and stir in grated cheese. Add a little of the hot mixture to beaten egg yolk. Add egg mixture back into the sauce; pour into a buttered baking dish. Carefully place onto the sauce 6 eggs. Cover and bake at 375°F until eggs are set as you like them.