Let the puff pastry rest at room temperature for about 10 minutes. Preheat oven (electric cooker: 225 °C/circulating air: 200 °C/gas: see manufacturer). Wash and halve the tomatoes. Wash basil, shake dry and pluck the leaves from the stalks.
Pluck Parma ham smaller.
Place the puff pastry with baking paper on a baking tray. Spread with pizza tomatoes, leaving about 2 cm of edge free. Spread tomatoes and ham on top. Season with pepper and sprinkle with vinegar and oil.
Bake in a hot oven for 8-10 minutes. Spread the olives on the dough and bake for about 5 minutes. Remove the pizza from the oven, sprinkle with basil and serve.