Wash and peel the asparagus and cut off the woody ends. Cut the rest into pieces approx. 2 cm long.
Boil the asparagus peels in 1.5 liters of water together with 2 tablespoons of salt and one tablespoon of sugar and continue cooking for 20 minutes. Then drain through a sieve.
Peel and finely dice shallots. Heat the olive oil in a saucepan and sauté the shallots in it. Deglaze with the asparagus stock, bring to the boil and cook the asparagus pieces in it for about 15 minutes. Stir the crème légère into the soup, bring to the boil, stir in the sauce thickener and simmer for about 5 minutes. Then finely puree the soup with a hand blender and season with salt, sugar and pepper. Depending on the taste and consistency, use a little more sauce thickener and let it simmer.
In the meantime, boil the eggs for about 8 minutes, then peel and chop. Chop the parsley too.
Arrange the soup in deep plates and sprinkle with egg and parsley.