Spread the mayonnaise on the slices of bread. Place in this order the slices of Caciocavallo cheese, the onion slices, the asparagus, the 2 slices of ham and finish with the 2 slices of cheese left. Add the second slice of pumpernickel bread to close the sandwich.
Heat a non-stick pan over medium heat. Brown the grilled cheese 2 to 3 minutes on each side and finish cooking it in the oven, for 4 minutes. Serve right away.
