Heat the oil in a large saucepan over medium heat. Add the onion and fennel and cook for 3-4 minutes until the onion is translucent. Stirring occasionally.
Add the potatoes, water, tomato juice, bay leaf and a strong pinch of salt. Reduce the heat and simmer with the lid closed for 25 minutes until the vegetables are soft. Stir occasionally.
Let the soup cool down a bit, then puree in portions in a blender or with a hand blender.
Return the soup to the pot, add the prawns and let them warm over a low heat for about 10 minutes. The soup takes on the shrimp aroma.
Stir in tomatoes and dill, season with salt and pepper and, if necessary, dilute with a little tomato juice.
Fill into preheated plates, garnish with dill tips or fennel greens and serve.