Peel and chop the onion. Heat the oil in a large pot. Fry the onion in it. 3⁄4 Pour l water and bring to the boil. Meanwhile peel, wash and roughly dice the turnip and potatoes. Add rutabaga, potatoes and stock.
Cover and simmer for about 20 minutes.
In the meantime, roughly chop the walnuts, roast them in a pan without fat and take them out. Clean, wash, drain and coarsely chop the arugula. Mix pesto, nuts and rocket, up to 1 tablespoon each. Season to taste with salt and pepper.
Finely puree the soup with a hand blender. Stir in cream. Season to taste with salt and pepper. Serve the soup. Garnish with pesto, rest of rocket and nuts.