Heat a heavy-based saucepan over medium-high heat, add olive oil and sauté shallots until transparent.
Add asparagus (be sure to cut off bottom portion that is hard and stalky) and tarragon leaves (reserve stems for later use) and cook briefly. Season with salt and pepper.
Deglaze pan with white wine and simmer until reduced by half. Add vegetable stock and continue to cook until asparagus is completely soft. Puree tarragon stems in a blender until completely smooth. Pour through a fine strainer and recheck seasoning.
Whip cream until firm. Gently fold in lemon zest, 1 teaspoon lemon juice and chopped tarragon stems.
Pour soup into 4 warm bowls and top with a dollop of cream.