What sets this version apart is that the filling is not cured and firm but soft, cold, and barely set, so the hot pillow does the opposite of what it does to a slice of meat: it slackens a cheese that is already almost a liquid. The base is gnocco fritto, the Emilian leavened dough that balloons in hot fat into a hollow, blistered, airy pillow. Squacquerone is the Romagnola fresh cow's-milk cheese so soft it spreads like thick cream and so mild it reads as little more than tang and milk. Smeared into the hot pillow it goes from cool and slack to warm and pourable almost at once, sinking into the crackling shell rather than sitting on it, the heat thinning the cheese into the bread and lifting its faint sourness against the bland fried dough.
The craft is the contrast of temperature and texture, and the order of assembly. The squacquerone is kept cold until the last second so the difference between the chilled cheese and the just-fried bread is at its sharpest, and it is spread rather than sliced because it has no structure to slice; it is essentially applied like a soft dressing onto the inside of the torn pillow. The dough is plain and salty and faintly steaming, which is exactly what a near-flavourless fresh cheese needs underneath it, a hot, fatty, bland base that gives the tang somewhere to register. It is built and eaten immediately, because both halves are fleeting in the same instant: the pillow before it collapses, and the cheese before it loses the cold edge that makes the contrast work. A few leaves of rocket are sometimes added for a bitter note, but the sandwich is essentially two textures meeting once.
The variations are the cured-meat versions of the same hot pillow rather than other soft cheeses: gnocco fritto with prosciutto, with mixed salumi, and the plain gnocco fritto on its own. Each of those deserves its own article rather than being crowded in here.