Peel the kohlrabi and potatoes and cut them into cubes. Peel and dice the onion.
In a large saucepan, sauté the onion in 1 tablespoon of oil until translucent. Add the potatoes and kohlrabi. Deglaze with broth, cook for 10-15 minutes until soft and season.
In the meantime, rinse off the wild garlic, pat dry, puree with the remaining oil and walnuts, stir in the pecorino cheese and season slightly.
Wash and halve tomatoes, core and dice.
Puree the soup, stir in the cream and season to taste again.
Divide the kohlrabi soup into plates, garnish with pesto and tomatoes and serve immediately!