Bake at 350° F.
Cut ham and cheese slices diagonally into 4 triangles each. Arrange 4 ham triangles around the sides of 8 individual buttered ramekins or baked custard dishes (6 to 8-ounce size.) Layer 4 triangles of cheese on top of ham.
Pour a tablespoon of cream into each dish. Carefully break an egg into each dish. Sprinkle each with seasonings and 1-1/2 teaspoons grated cheese.
Place cups in a shallow pan, then pour hot water in pan to depth of 1 inch. Bake for 20 to 25 minutes, or until egg sets and cheese is melted. To serve, invert an egg over each muffin half.