Place the water in a large skillet over medium-high heat.
When the water is at a shiver, add the asparagus spears and blanch for 8-10 minutes.
While the asparagus is blanching, fill a large bowl with ice water.
When the asparagus is done, place immediately into ice water and chill for 10 minutes.
While the asparagus is chilling, place the olive oil in a large skillet over medium-high heat.
Add the onion and tarragon and cook slowly for about 10 minutes, adjusting the heat so that the onions become soft and translucent but do not brown.
Cut the chilled asparagus into 1 inch chunks (reserving a few asparagus tips for garnish, if desired), then place the asparagus, salt, water, honey, milk and cooked onions into a blender.
Puree until very smooth.
Reheat gently and serve.