The French toast sandwich is the rare American breakfast build where the bread is cooked twice, and that double cook is the whole sandwich. Two slices are dipped in an egg-and-milk custard and griddled in butter before anything goes between them, so the carrier arrives already rich, already sweet at the edges, already a finished thing on its own. Everything stacked inside has to argue with that, which is why the filling skews salty: a folded egg, a few strips of bacon, a breakfast sausage patty, a slice of ham. The custard-soaked exterior is the flavor headline and the savory center is the counterweight, not the other way around.
The craft is in the custard ratio and the heat. Too much milk and the slices go to mush under their own filling; too little egg and the surface will not set into a tender, faintly crisp face. The bread is cut thick on purpose, a sturdy white or brioche, so the custard saturates the crumb without collapsing it and the slice can still take a load. It is griddled low and patient so the interior cooks through before the butter scorches the outside, the same timing problem a grilled cheese poses, run sweet. The filling goes against the hot cooked faces straight off the griddle so the cheese melts and the egg sets against the bread before it cools, because a French toast sandwich eaten warm is a different and better thing than one that has gone slack on the plate. Maple syrup is the open question: served on the side for dipping, or brushed inside as the sauce that ties the sweet shell to the salty middle.
The variations stay inside that sweet-shell, savory-center frame. The Monte Cristo is the codified cousin, a ham-and-cheese battered and griddled into the same logic and dusted with sugar. A stuffed build runs cream cheese and fruit and pushes the thing fully toward dessert; a fried-chicken-and-syrup version borrows the chicken-and-waffles argument and sets it between custarded slices. Each of those is its own codified build and deserves its own article rather than being crowded in here.