Peel and finely chop the onion. Peel, wash and dice the turnip and sweet potato. Heat the oil in a pot and fry the diced onion until transparent. Add diced turnip and potatoes and steam for 8-10 minutes, stirring several times.
Deglaze with vegetable stock and cook for about 15 minutes at low heat. Finely puree the soup with a blender. Stir in milk and cream and season with salt and pepper. Heat 1 tablespoon of olive oil in a pan, roast the walnuts in it, take them out, chop them and put something aside for garnishing.
Clean and wash the rocket, put 4 leaves aside for garnishing, chop the rest roughly. Peel garlic clove and chop finely. Grate parmesan finely. Finely mash the walnuts, except for a little for garnishing, 5 tbsp. olive oil, rocket, garlic and Parmesan cheese, season to taste with salt and pepper. Arrange the soup in plates, garnish with walnuts, rocket and pesto.