1. In a large pot sauté onions in vegetable oil over low heat, stirring frequently, until translucent. Do not let them get burned. Salt it lightly to help tenderize them. The onion should be cut into very-very small pieces. 2. (If you make it with meat, add it now, season with salt and ground black pepper. Stir constantly for about 3 minutes or until the meat has been seared on all sides.) 3. Add the carrots, the parsley root and the celery root cubes. 4. Add 1300 ml water, cover and after 10 minutes of cooking add the green peas and the mushrooms and cook until vegetables (and meat) are tender. 5. Remove the pot from the heat. In a bowl mix the heavy cream with some soup liquid and pour this mixture back to the soup pot. Add tarragon and bring back it to a boil. When it starts boiling, turn the heat off and add lemon juice.