1In a shallow bowl, whisk together the 4 eggs and 1 cup of milk until well combined.
Gradually add the 1 cup of all-purpose flour to the egg mixture, whisking until smooth and free of lumps.
Spread 1 tablespoon of mayonnaise on one side of each slice of brioche bread.
On four slices of bread, layer 1 slice of cheddar cheese, 1 slice of cooked bacon, and 1 fried egg.
Top each with another slice of bread, mayonnaise side down, to form a sandwich.
Heat 1 tablespoon of butter in a large skillet over medium heat.
Dip each sandwich into the egg batter, ensuring both sides are well coated.
Place the sandwiches in the skillet and cook until golden brown on both sides and the cheese is melted, about 3-4 minutes per side.
Serve the sandwiches warm, drizzled with 1 tablespoon of maple syrup per sandwich.