Bring 1 1/4 liters of water to the boil. Add the bean kernels.
Cut the savoy cabbage into narrow strips, chop the celery. Peel and dice the tomatoes. Peel the potatoes, also cut into cubes. Finely chop the spinach and chard. Chop the onion, mash the garlic. Add the prepared vegetables to the pot. Salt, pepper and simmer over a moderate heat for 25-30 minutes. The vegetables should be done, but not disintegrated.
In the meantime, prepare the pasta according to the instructions on the packet. Add to the soup with the parsley. Finally stir in the pesto, heat again. Serve the soup and garnish with the chopped basil.