Brush the potatoes thoroughly and cook with the skin in salted water for about 20 minutes. Then drain and cut in half lengthways. Fry the potato halves in hot olive oil until golden brown. Season with salt and pepper and let cool down a little.
In the meantime, wash the tomatoes and cut them in half. Pluck the basil leaves and chop them if necessary.
Arrange the potato halves with the tomatoes and basil on plates. Drizzle the dressing over the salad and serve sprinkled with sesame seeds.