Wash the asparagus and cut off the woody ends. Cut the asparagus into pieces, leaving the asparagus tips aside. Peel and finely chop the onions and garlic.
Heat 2 tablespoons of oil in a large pot. Fry the asparagus, onions and garlic in it. Pour on 1 1⁄4 l water. Add broth, 1 tsp. sugar and frozen peas. Bring to the boil and simmer covered for about 15 minutes.
Wash tarragon and shake dry, pluck the leaves and chop finely. Add tarragon to the soup about 5 minutes before the end of the cooking time.
Heat 1 tablespoon of oil in a frying pan. Fry the asparagus tips for 3-4 minutes, season with salt and pepper. Puree the soup finely with a hand blender. Season with salt, pepper and balsamic vinegar to taste.
Arrange and decorate with liquid cream. Spread the asparagus tips on top. Cut the cress from the bed and sprinkle over it. Sprinkle with olive oil.