The thing this sandwich is built around is the bread, and specifically what the oil and salt of a Genoese focaccia do once a cheese is folded into it. Focaccia genovese is the thin, dimpled kind: a slack dough proved low and wide, the surface pocked with finger holes that hold a brine of salty water and a flood of olive oil, baked until the top is gold and faintly chewy and the crumb stays slick. Split horizontally and laid with a soft cheese, usually stracchino or another fresh cow's-milk cheese with a milky tang, it becomes a sandwich in which the filling barely has to do anything. The oil has already seasoned the crumb through, the salt is already in every bite, and the cheese reads as the cool, lactic centre against bread that is doing the louder work.
The craft is the ratio of fat to crumb and the choice of a cheese that will not fight it. The focaccia is kept thin so the oiled surfaces are close together and the cheese sits in a shallow band rather than a thick slab, which is what keeps the thing from sliding into grease. A fresh cheese is the right choice precisely because it is mild and spreadable: stracchino slackens slightly against bread still holding a little oven warmth, smoothing into the crumb instead of perching on it as a separate layer. An aged or assertive cheese would argue with the salt of the focaccia and turn the bite into a contest; the soft cheese yields to it. Assembly is fast and the sandwich is eaten close to when it is made, while the bread is at its best and before the oil has had time to weigh the crumb down into something dense.
The variations stay in Liguria and stay close to the same logic of one cheese on the oiled bread: the version with a sharper fresh cheese, the one finished with a few leaves of rocket or a turn of pepper, the focaccia di Recco with cheese sealed inside two unleavened sheets rather than split into one. The last is really a separate bread and a separate technique. Each of those deserves its own article rather than being crowded in here.