First cut or snap off the woody ends, then thickly peel and slice the rest of the asparagus (leaving the tips whole). Boil the peelings and ends for 10 minutes in 750 ml water with the sugar and some salt added to taste.
Meanwhile melt the butter in a soup pot and stir-fry the sliced asparagus on a high heat (saving the tips for later), add the cream and reduce slightly.
Strain the water with the peelings and add this liquid to the stir-fried slices, together with the white wine.
Bring everything to the boil and let simmer for 10 minutes, then purée the soup thoroughly with the hand blender.
Add the asparagus tips and let the soup simmer for another 2-4 minutes. 'Season well to taste.
Divide into 4 portions and sprinkle with the tarragon.
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