Wash the potatoes and cook in boiling water for about 15 minutes. Drain, quench, peel and slice. Drain olives and cut into rings. Heat the oil in an ovenproof pan (18 cm Ø) and fry the potatoes.
Add the olives. Whisk eggs and milk together. Season with salt and pepper and pour over the potatoes. Put the tortilla in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) and let it stand for 10-15 minutes.
Wash the tomatoes. Wash basil, shake dry and pluck leaves from stems. Cut the tortilla into approx. 20 cubes (each approx. 2.5 x 2.5 cm). Put the tomatoes on the dices and place a basil leaf on top.
Halve the ham slices and roll them up. Place the ham on the basil and pin it with a wooden skewer.