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 1-2 tablespoons of oil in a large pot. Sauté the asparagus, onions and garlic for about 2 minutes, dust with sugar and allow to caramelize slightly, deglaze with vinegar. Add deep-frozen peas, 1 teaspoon salt and a little pepper, pour on broth and simmer covered for about 15 minutes.
Wash tarragon, shake dry and chop finely. Add tarragon to the soup about 5 minutes before the end of the cooking time and puree finely. Season cream with salt and pepper. Heat 1 tablespoon of oil in a frying pan, fry the asparagus tips for approx. 3 minutes while turning, season with salt and pepper. Arrange the soup in plates and decorate with the cream. Sprinkle cress and asparagus tips on top and drizzle with olive oil.