Let the puff pastry rest at room temperature for about 10 minutes. Preheat oven (electric cooker: 250 °C/circulating air: 225 °C/gas: see manufacturer). Wash and halve the tomatoes. Wash basil, shake dry and pluck the leaves.
Fold the short side of the puff pastry halfway down, place it on a baking tray lined with baking paper and roll out slightly larger (approx. 20 x 30 cm). Spread with chunky tomatoes, leaving about 2 cm free around the edges.
Spread the tomatoes on the dough. Drizzle with vinegar and 2 tablespoons of oil.
Bake in the hot oven on the lower shelf for about 10 minutes. Pluck the ham into pieces. Remove quiche from oven. Spread olives and ham on top and bake for about 5 minutes. Pluck the mozzarella into pieces and spread on the quiche.
Sprinkle with 1 tablespoon of oil and season with pepper. Sprinkle with basil.