Make the French toast. Preheat oven to 350°F. Break eggs into a medium mixing bowl. Add sugar, milk, and salt and whisk lightly.
Prepare a large skillet over medium heat with a little bit of butter to coat the pan.
Place bread slices in egg mixture one at a time, allowing each to soak up moisture for a few seconds. The bread needs to go directly from the egg mixture to the hot pan, so only soak as many slices at a time as the pan will fit.
Sear each slice in the pan until golden brown on both sides. Continue until all the bread is soaked and seared.
Assemble the sandwich. Start with one piece of French toast topped with two slices of bacon, a fried egg, and a slice of cheddar, closed off with another piece of French toast.
Place the whole sandwich in the oven until cheese is melted. Serve with a side of maple syrup.