The panino con taralli is a sandwich built around a sound: the snap. Taralli are the small ring-shaped savoury crackers of Puglia, made from flour, oil, and white wine, boiled then baked until they are hard and brittle all the way through, often scented with fennel seed or black pepper. Worked into a panino, crushed across the filling rather than eaten alongside, they become a layer of pure crunch in a sandwich that would otherwise be soft. That deliberate addition of a hard, shattering texture is the whole idea. It is the Puglian instinct to give a soft filling something that breaks against the teeth, without reaching for a toasted bread to do it.
The craft is keeping the crunch alive and choosing what it sits against. Taralli go stale in the worst direction, turning from crisp to merely hard, so they are crushed in coarse and added at the last moment; folded in early they draw moisture from the filling and lose the snap that was the entire reason for them. They want a soft, slightly moist partner to contrast against, a fresh cheese, a creamy spread, a ripe tomato, since a dry filling plus a dry cracker is just two dry things. The bread is kept plain and soft on purpose; the texture event is supposed to come from the crushed rings, so a hard crust would only compete with them. Salt is rarely needed because the taralli are already seasoned, and the fennel or pepper baked into them often becomes the dominant aromatic of the whole sandwich.
The named variations turn on what soft thing the crunch is set against. There is the build with stracciatella or a fresh cheese, the version over a tomato-and-oil dressing, and the taralli scattered into a friselle-style assembly for a double crunch. The taralli eaten as they usually are, on their own with a glass of wine, are a different ritual entirely and deserve their own article rather than being crowded in here.