Rinse asparagus and snap off and discard tough ends. Coarsely chop asparagus.
In a 4- to 5-quart pan over medium heat, stir olive oil and shallots until shallots are limp, about 3 minutes. Add asparagus, 1 1/2 tablespoons tarragon, vegetable broth, and 2 cups water. Bring to boiling over high heat and cook until asparagus is tender-crisp when pierced, about 3 minutes longer.
Meanwhile, whip cream until it holds soft peaks.
In a blender, purée soup until smooth, a portion at a time. Season to taste with salt.
Return soup to pan and stir over high heat until steaming. Ladle into bowls, and sprinkle with remaining tarragon.
Add an equal portion of whipped cream to each bowl.