The panino con frittata turns a cooked egg into a sliceable cold cut. The Italian frittata is not the folded, soft-centred French omelette: it is set firm all the way through, cooked flat in a pan and finished so it holds together as a single disc, then left to cool. Cold and firm is the operative state. Once it has rested it can be cut into a slab the size of the bread and laid in like a slice of mortadella, which is exactly how it goes into the panino. That is the whole trick of this sandwich: the filling is not a wet egg that weeps into the crumb but a solid, room-temperature wedge with its own structure, which is why it travels in a bag to a worksite or a beach and is still intact at lunch.
The craft is in setting the egg dense enough to behave like a slice. The frittata is loaded with one developed thing, sautéed onion, potato cooked through, courgette wilted and drained, so it carries flavour without releasing liquid later; raw or barely-cooked vegetables would steam inside the egg and turn it weepy in the bread. It is cooked slowly and turned so it sets evenly rather than browning hard on one face, and it is cut to the footprint of the roll so the bite is even and nothing hangs out the side. The bread is plain and sturdy, a rosetta or a length of ciabatta, because the egg slab is already a finished thing and a strong loaf would only argue with it. No sauce is wanted; at most a little oil or a leaf where the egg runs lean.
The variations are the frittata repertoire itself, each its own preparation rather than a footnote here: the onion frittata di cipolle, the potato version, the green frittata di erbe, and the Neapolitan leftover-pasta cake folded into bread, which is the Panino con Frittata di Pasta and a different argument entirely. Each is one set egg given a loaf, and each deserves its own article rather than being crowded in here.