Wash the potatoes and cook in boiling water for about 20 minutes. In the meantime peel onions and cut them into slices. Drain potatoes, rinse and peel. Cut into thin slices.
Heat 4 tablespoons of oil in a pot and sauté the onions in it. Deglaze with vegetable stock. Season to taste with salt and pepper. Add vinegar. Pour marinade over the potatoes and fold in carefully.
Allow to soak for about 30 minutes. In the meantime, wash the basil, dab dry and, except for a few leaves for garnishing, pluck the basil. Roast pine nuts in a pan without fat until golden brown. Put the basil, pine nuts, except for a few for garnishing, parmesan and the rest of the olive oil into a universal chopper and process into a pesto.
Season with salt and pepper. Clean, wash and drain the arugula. Cut tomatoes into small pieces. Mix potato salad with rocket, green and black olives and tomatoes. Arrange salad on a plate, sprinkle with pine nuts and sprinkle with pesto.
Garnish with the remaining basil. Add extra pesto.