Croque Madame

Directions

1. 1
   Preheat oven to 400 degrees F.
2. 2
   Butter 1 side of each bread slice.
3. 3
   Set half of the slices of bread buttered side down in the griddle or cast iron skillet, and cover each with a slice of cheese. Place 3 or 4 slices of the ham over the cheese, and place the top slice of bread over the ham, buttered side up.
4. 4
   Heat griddle or skillet over medium heat. Cook sandwiches until bottom is golden brown and cheese is melted, about 3 minutes per side. Remove sandwiches and place on a plate.
5. 5
   Spread a thin layer of mayonnaise on the top of each sandwich, and then place a slice of cheese on top. Put the sandwiches back onto the griddle or skillet then place in oven, cooking until golden brown and cheese is melted, about 5 minutes.
6. 6
   Melt 1 tablespoon butter in skillet over high heat. Cook each egg sunny side up. Turn egg over and cook 3 minutes longer for a soft-cooked egg, or 5 minutes longer for a hard-cooked egg. Repeat with remaining butter and eggs.
7. 7
   Place 1 fried egg atop each sandwich. Season egg, to taste, with salt and pepper. Serve sandwich immediately.