This is a Roman secondo folded into bread, and the thing that defines it is that the meat is already a finished dish before it ever meets the loaf. Saltimbocca alla romana is a thin veal escalope with a slice of prosciutto and a sage leaf pressed onto it, cooked fast in butter and finished with white wine into a glossy pan sauce. Put that between bread and the sandwich's whole problem becomes the sauce: a wet, buttery, wine-loosened thing that wants to run straight out the sides. The prosciutto is bonded to the veal so the salt and fat sit inside the meat rather than as a separate layer, which is why a single escalope reads as one cohesive filling and not a stack.
The craft is making a saucy pan dish behave between two pieces of bread. The veal is pounded thin so it cooks in under a minute and stays tender, and the prosciutto is pressed hard onto it so the two cook as one and do not separate in the hand. The pan sauce is reduced past the point you would leave it for a plate, tighter and more syrupy, so it glosses the meat instead of flooding the crumb. The bread is a sturdy roll, often a rosetta or a crusted ciabatta, and its cut face is sometimes brushed with that reduced sauce so the bread carries the butter and wine deliberately rather than soaking it by accident. The sage stays on, one leaf, because it is the aromatic that names the dish. It is eaten warm, soon, while the sauce is still set and the veal still soft.
The variations are the Roman repertoire given the same treatment rather than changes to this one. There is the version with a thin slice of cheese melted under the prosciutto, the chicken-escalope build for a cheaper cut, and the related Roman braises spooned into bread the same way. The trapizzino tradition that carries those braises is a different structure entirely, and those deserve their own articles rather than being crowded in here.