The wrap italiano takes the soft folded-flatbread idea and argues it with an Italian larder, so the bread and the fillings are chosen to suit each other. The wrapper is a piadina-style flatbread, a thin unleavened or barely leavened round of wheat flour, water, and lard or olive oil, cooked fast on a hot griddle until it is supple and faintly blistered but still pliable enough to roll without cracking. Inside go the things an Italian deli already has on hand: cured salumi such as prosciutto crudo or salame, fresh mozzarella or squacquerone, grilled or roasted vegetables, rocket, and often a smear of pesto. The flatbread is deliberately mild and a little chewy so it carries the salt and fat of the fill rather than competing with it, and the fill is balanced wet against dry so the roll holds its shape in the hand.
The craft is in the flatbread's pliability and in controlling moisture so the roll does not go soggy or split. A good piadina for this use is cooked through but kept soft and slightly elastic, warm when it is filled so it folds around the contents instead of fracturing at the seam; a brittle, overcooked round will not roll and a doughy underbaked one turns to paste. The fillings are layered with the wet element, the mozzarella or the pesto, kept off the outer edge so the seam stays dry and the wrap can be cut without spilling, and the grilled vegetables are drained well because aubergine and zucchine hold oil that will otherwise pool. The salt comes from the salumi, so the dressing stays restrained: pesto or good oil, not a heavy sauce. A sloppy build overfills the centre, wraps a cold stiff flatbread, and lets watery vegetables soak the seam until it tears.
The near relations are a wide family and each deserves its own article rather than being crowded in here. There is the Romagnol piadina farcita folded rather than rolled and eaten in its home region, the crescione which seals the same flatbread around a filling and griddles it closed, and the larger tortilla-style wrap that borrows the format but drops the Italian shelf entirely. Each is a different flatbread argued in its own place, and each is its own subject.