Pesto e fagiolini borrows its logic from a plate of Ligurian pasta, where the green beans are not a side but a structural part of the dish, cooked with the trofie and dressed in the same pesto. Carried into bread, the green beans do the same job: they give the sandwich its body. The defining fact is that this is not pesto spread on a roll with a few beans added for show. The fagiolini are the bulk, and the basil sauce is the bind that coats them and glues the whole loose construction to the crumb. Without the beans it is a smear; without the pesto it is a handful of vegetables. The two are engineered to need each other.
The craft is cooking the beans right and using the pesto as mortar. The fagiolini are boiled just to tender, still with a faint snap, then cooled and dried so they do not weep into the bread, and cut to a length that sits in the roll rather than sticking out of it. The pesto, the raw Genovese sauce of basil, pine nuts, garlic, pecorino, and oil, is used generously enough to film every bean and seal the inner crumb so the sandwich holds together in the hand. That waterproofing is the real reason the sauce is structural rather than only flavour: it stops a wet vegetable from collapsing the bread. The loaf is plain and takes oil-dressed fillings well, often a chewy roll, and nothing else is needed because the pesto already carries cheese, fat, and salt within it.
The variations stay Ligurian and follow the same pasta plate. There is the version with a few waxy potato slices added, the second half of that classic dish, the one with green beans alone for a leaner build, and the relative that swaps the beans for another boiled vegetable under the same sauce. Each is the same pesto-as-bind idea with one element changed, and each deserves its own article rather than being crowded in here.