Add the mustard and cheese to the well seasoned white sauce and stir until the cheese is melted. Cover the bottom of a 6 1/2 x 10 inch baking pan with half the sauce. Carefully break the eggs into sauce; cover with the remaining sauce. Bake in a moderate oven 325 degrees for 20 to 25 minutes, depending upon how well done you like your eggs. Serves 3-6.