The panino con salsa tartufata is built around a paste, not a shaving, and the paste is the entire argument. Salsa tartufata is a dark, dense spread of finely chopped mushroom carrying a measured amount of truffle, usually the Umbrian black, bound in oil into something stable and spreadable. It exists to solve a problem fresh truffle creates: the aroma is fierce, short-lived, and ruinous in excess, and a worked paste holds a controlled fraction of it in suspension so it can be spread evenly and kept. The defining quality of this sandwich is therefore restraint made physical: the truffle is already dosed and tamed before it reaches the bread.
The craft is measure and what the paste is set against. Salsa tartufata is spread thin, a film rather than a layer, because even tamed the truffle note tips quickly from haunting into bitter and metallic if there is too much of it. It wants a carrier of fat to bloom into, which is why it is most often met with a soft mild cheese, a film of butter, or a barely warmed egg rather than a lean meat that gives the aroma nothing to hold. The bread is plain and the warmth gentle: a little heat lifts the volatile scent, but real heat scorches it, and an assertive loaf would bury a flavour that works by suggestion. It is assembled close to eating, because the mushroom base keeps far better than fresh truffle but the aromatic top note still fades the longer it sits open.
The variations are the contemporary paninoteca working the same volatile ingredient from different angles, and each is its own subject. The fresh-shaved seasonal truffle build for when the season is in, the truffle-and-cheese panino, the truffle laid over a soft egg, the gourmet version that lifts the components around it. Each strikes its own balance of quantity against carrier, and the worked-paste salsa tartufata sits apart as the restrained, keepable reading. Each of those deserves its own article rather than being crowded in here.