A near-guaranteed hangover helper. No need to choose between the "griddle" and "egg" section on a brunch menu, when you can have both. Covering the fried eggs just before the whites set is an easy way to avoid overcooking the eggs while keeping the yolks runny.
Whisk together the milk, syrup, cinnamon, vanilla, and 2 eggs in a shallow dish. Soak the bread slices until saturated, about 5 minutes per side, soaking in batches if needed. Heat 1 tablespoon of the butter in a large pan over medium-high heat until foamy. Add the bread, in batches if needed, and fry until golden brown on both sides, 3 to 4 minutes per side. Meanwhile, heat the remaining butter in a frying pan over medium-high heat until hot. Gently crack the remaining eggs into the pan. Sprinkle with salt and pepper, and fry, gently lifting occasionally so eggs don't stick, until whites are almost set, 1 to 2 minutes. Lay cheese over eggs and cover with a lid until cheese is melted and whites are cooked through, about 1 minute longer. Divide the cheesy fried eggs between 2 slices of French toast, and top with the remaining slices.