The matzo ball soup sandwich is a sandwich made from a dish that was never meant to leave the bowl, and that translation is the whole of it. Matzo ball soup is a liquid food: a poached dumpling of matzo meal and egg sitting in clear chicken broth. Turning it into a sandwich means giving up the broth entirely and treating the matzo ball as a solid filling, which is a structural decision the soup itself resists. The sandwich exists only at the delis willing to make that decision, and what defines it is the absence of the liquid that defines its source.
The craft is in handling a filling that has no structure of its own. The matzo ball is dense and tender, somewhere between bread and dumpling, so it is sliced or halved and laid flat rather than left whole, because a sphere will not stay on bread. It is set with poached or pulled chicken from the same pot, the pairing that the soup already implies, and the bread has to be soft enough not to fight a soft filling: a plain rye or a soft roll, not a hard crust. The broth cannot go in or the sandwich dissolves, so the moisture it would have carried is replaced by a smear of schmaltz, a little of the chicken's own fat, or a spoon of the dumpling's poaching liquid worked in just to the edge of wetness. Salt, pepper, and sometimes dill stand in for the seasoning the broth used to do. It is a niche build, made to order where someone asks for it, and it reads as the soup deconstructed onto bread rather than as a codified deli standard.
The variations are few and mostly a matter of the carrier and the bind. A version on soft rye runs leaner; a version with extra schmaltz or a swipe of chicken salad pushes it richer to make up for the missing broth. It belongs to the dense long tail of regional deli specialties built around a structural decision a chain would never make, and the broader Jewish deli shelf it comes from deserves its own article rather than being crowded in here.