The panino con vitello tonnato is a plated Piedmontese dish folded into bread, and what defines it is the sauce, not the meat. Vitello tonnato is cold poached veal sliced thin under a tonnato sauce, a smooth emulsion of tuna, anchovy, capers, and either mayonnaise or the cooking liquor whipped together. On the plate the veal is the centrepiece; in a sandwich the sauce becomes the structural element. It is what seasons the otherwise lean, mild cold veal, binds the slices to each other and to the crumb, and turns a knife-and-fork dish into something a hand can hold. The meat supplies the texture and the bulk; the tonnato supplies the flavour and the glue.
The craft is making a cold composed dish behave between two slices. The veal is poached, cooled, and sliced as thin as it will hold, because thick slices in a sandwich read as a chewy block and waste the point of the dish; thin, supple sheets layer cleanly and take the sauce on every face. The tonnato is made thick on purpose, stiffer than it would be plated, so it sets against the cold meat and holds the structure rather than running out of the bread and softening the crumb. The bread is chosen sturdy and is sometimes lightly toasted to survive the moisture, and the portion is controlled, because an overfilled one fails at the first bite and the whole idea is a delicate dish made portable, not a heavy one. It is served cold throughout, the sauce setting firmest at fridge temperature, which is the only state in which it works.
The variations are mostly about the sauce and the cut: the mayonnaise-rich modern tonnato against the older cooking-liquor emulsion, the version with extra capers worked in, the build that leans leaner on the veal. Each is the same cold dish given a handle, and each deserves its own article rather than being crowded in here.