The panino con bagnet vert is defined by its sauce before anything else, and the sauce is the Piedmontese green one: bagnet vert, a raw blend of parsley, anchovy, garlic, capers, and breadcrumb bound loose with olive oil and sharpened with vinegar. On the plate it is the classic dressing for boiled meats; as a sandwich it is the bagnet that runs the show. It is herbal and sharp, salty from the anchovy and the caper, acidic from the vinegar, with a coarse, almost gritty texture from the parsley and crumb. Spread onto a roll with cold sliced boiled beef or tongue, it is the green sauce that decides how the sandwich tastes; the meat is the surface it acts on.
The craft is keeping the sauce fresh and matching it to a bread that holds. Bagnet vert is not cooked, so its brightness comes from the raw parsley and the bite of fresh garlic, which means it is best made close to assembly before the green dulls and the vinegar flattens. It is bound only thick enough to spread without running, because a sauce loosened with too much oil will soak the crumb; a crusted roll or a firm country slice gives it the structure it needs. The boiled meat it dresses, typically a lean cut from the bollito, is sliced thin and cool so the warm sharpness of the sauce reads against it cleanly. The anchovy and the caper are doing the salt and the depth; the vinegar is doing the cut through the fat, exactly the work it does at the table moved into bread.
The variations stay Piedmontese and each is its own preparation rather than a footnote here. There is the version heavier on anchovy for a deeper salt, the one with hard-boiled egg worked into the sauce for body, the milder one with more crumb. Its direct counterpart, the red pepper-and-tomato sauce of bagnet ross, is the other sauce of the bollito table and a different idea entirely; that and the mixed boiled meats it accompanies follow their own logic and deserve their own articles rather than being crowded in here.