In a large bowl, whisk together the eggs, milk, vanilla extract, cinnamon, and salt until well combined.
Preheat a skillet or griddle over medium heat and add a tablespoon of butter.
Dip each slice of bread into the egg mixture, allowing it to soak for a few seconds on each side.
Place the soaked bread slices onto the skillet and cook for about 3-4 minutes on each side, or until golden brown.
Once the bread is cooked, place a slice of cheese on top of two pieces of the French toast. Add the bacon or sausage on top of the cheese, then top with the remaining French toast slices to create a sandwich.
Cook the sandwiches for an additional 1-2 minutes on each side, pressing down gently, until the cheese is melted.
Serve warm with maple syrup if desired.