- 8 slices sourdough bread
- 8 ounces gruyere, very thinly sliced
- 12 ounces smoked ham, very thinly sliced
- 2 -3 tablespoons mayonnaise
- 5 tablespoons unsalted butter
- 4 extra-large eggs
- salt and pepper
- Preheat oven to 400 degrees F.
- Butter 1 side of each bread slice.
- 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.
- 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.
- 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.
- 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.
- Place 1 fried egg atop each sandwich. Season egg, to taste, with salt and pepper. Serve sandwich immediately.