Bake the bacon on a broiler pan or a rack set over a baking sheet at 375 degrees until just crisp, about 20 minutes. Arrange 4 slices of bread with some cheese and the apples on top. Beat the eggs with the milk (or half-and-half) and a little nutmeg. Heat a large griddle pan over medium heat. When ready, arrange 3 slices of bacon on each sandwich and top with a little more cheese and 4 more slices of bread. Coat each sandwich in the egg batter. Grease the griddle with butter and griddle the sandwiches until deep golden on each side and the cheese has melted. Halve the sandwiches and drizzle with a little warm syrup.