The panino con radicchio rosso is the round-headed cousin of the Treviso sandwich, and the difference is the whole point. Here the chicory is the Chioggia-type red radicchio: a compact, near-spherical head of crisp white-veined crimson leaves, less aggressively bitter than the elongated Treviso and firm enough to hold its crunch raw. Because the bitterness is gentler and the texture is its own selling point, this radicchio is most often used uncooked, shredded or torn into the sandwich for snap and a clean bitter edge rather than grilled into sweetness. The build is decided by that choice: raw and crisp, where the Treviso version is charred and soft.
The craft is keeping the leaf crisp and dressing the bitterness without drowning it. The head is cut close to service so the cut edges do not wilt or rust, then dressed lightly with oil, a little vinegar, and salt so the bitter note is rounded but the crunch survives all the way to the bread. Raw radicchio weeps if it sits, so it is the last thing in and the bread is plain and sturdy enough not to go soft under it. The counter is usually a fatty, salty partner that the crisp bitterness can cut through: a soft cheese, a few folds of a cured meat, sometimes a sweet note like a smear of honey or a slice of pear to set against the chicory. The discipline is the same Italian one: one vegetable doing the structural work, treated correctly for its kind.
The variations track the raw leaf, each its own preparation rather than a footnote here: radicchio with gorgonzola and walnut for the sweet-blue counter; the lean cured-meat build where crunch cuts the fat; and the all-vegetable version dressed only in oil and vinegar. Each is the same raw-radicchio logic given a loaf, and each deserves its own article rather than being crowded in here.