Easy Croque-Madame (Ham and Grilled Cheese Sandwich with Fried Egg)

Make the sandwich: Spread both slices of bread with mayonnaise. Flip them over and spread the other side with mustard. Onto one slice of bread, layer a slice of cheese, the ham, and the other slice of cheese. Top with the other slice of bread, mustard-side down. (The mayonnaise sides should face out.) Sheryl Julian Fry the sandwiches: Melt the butter in a large skillet over medium heat, then add the sandwich. If you have a bacon press, grill press, or panini press, set it on top to weight the sandwich down (otherwise, just press a few times with the flat of your spatula during cooking). Cook for 3 minutes, or until the bottom slice of bread is golden. Carefully flip the sandwich in the skillet. Set the bacon press back on top (or press with the flat of your spatula), and cook another 3 minutes or until the underside is golden. Transfer to a plate. Sheryl Julian Sheryl Julian Fry the egg sunny-side up: Wipe out the skillet. Heat the olive oil in the skillet over medium heat until the oil shimmers and flows easily. Add the egg and cook for 1 minute exactly. Cover the skillet and cook for another 30 to 60 seconds, or until all the whites are set. (A runny yolk is preferred for this sandwich, however cook the egg for longer if you prefer a more hard-cooked yolk.) Serve: Slide the egg onto the top of the sandwich. Sprinkle with salt and pepper, along with thyme or parsley. Serve immediately.