The toast quattro formaggi drops the ham that usually anchors the Italian griddled bar sandwich and asks four cheeses to do the whole job between two slices of soft white bread. The defining fact is that this is a blend, not a pile of four separate cheeses. The point of using four is that each contributes a different property and no single one would carry the sandwich alone: a good melter for flow and the pull, a hard aged cheese for salt and depth, a soft fresh cheese for creaminess, and a blue or a washed-rind for the sharp note that keeps the whole thing from going flat and dull under heat. Pressed and griddled, they fuse into one molten interior. Use only one cheese and it is a plain melt; use four that all do the same thing and the extra three are wasted. The combination is the dish.
The craft is balancing the four so they melt together and no one of them dominates or seizes. The bread is pliable pane in cassetta, buttered on the outside so it browns evenly in the clamp. Inside, the melter goes in the largest share because it does the binding, the aged cheese is grated fine so it disperses rather than sitting in a hard lump, the fresh cheese is spread thin as a creamy layer, and the strong cheese is used sparingly because a blue or a pungent rind will swamp the others if it is more than an accent. The parcel is kept slim so the centre liquefies before the crust burns, and it is pressed just until the inside flows and pulls into a thread. A good toast quattro formaggi reads as one rich, layered cheese with a sharp lift at the back; a sloppy one is greasy and one-note because the cheeses were dumped in equal heavy amounts and never integrated, or scorched because the parcel was too thick to heat through.
The variations move one cheese or the bread while keeping the all-cheese logic, and each deserves its own article rather than being crowded in here. There is the prosciutto cotto and cheese build the format is named for, the smoked-salmon version that adds a cured fish to a soft cheese, the relative that folds in walnuts or a smear of honey against the blue, and the open grilled version finished under heat rather than clamped. Each is the same idea with one element changed.