Melt butter in saucepan over medium to medium-high heat and add onions and apples, cinnamon, bay, salt, pepper, a light sprinkle of nutmeg, sugar and lemon juice. Cook to sauce-like consistency stirring occasionally 20-25 minutes, douse with liquor.
Season pork (or chicken) with salt and pepper and coat with flour, egg beaten with milk and breadcrumbs seasoned with nutmeg and parsley. Shallow fry the cutlets in a thin layer of vegetable oil until crispy and golden. Squeeze lemon juice over top of cutlets just before you're ready to build the sandwiches.
Lightly toast the rolls under a broiler then divide the cutlets over the top of the toasted roll. Spoon some apple-onion mixture over the top of the cutlets then top with shredded cheese and broil until cheese is melted.