Wash the asparagus, cut off the ends. Cut the asparagus into narrow pieces. Put 1/3 of the stems in a pot with 1 litre of cold water and lemon juice. Season with a little salt and sugar, bring to the boil.
Cover and let it simmer at low heat for about 15 minutes. Add the white wine and stock about 5 minutes before the end of the cooking time. Puree everything. Grate parmesan and dissolve in the asparagus stock for about 2 minutes while stirring.
Pass the parmesan broth through a sieve into another pot. Boil up the soup. Add remaining asparagus pieces and simmer for about 3 minutes. Stir the starch in a little water until smooth, thicken the simmering soup with it while stirring.
Add cream. Simmer the soup for another 2-3 minutes. Season to taste with salt, pepper and sugar if necessary. Wrap Grissini sticks with Serrano ham and sprinkle with pepper. Arrange soup in deep plates, sprinkle with pesto.
Garnish with basil and parmesan. Serve with grissini sticks.