Step 1
Place the potatoes into a small pot with enough water to cover; bring to a boil then reduce heat to medium-low place a cover on the pot and simmer until tender about 20 minutes.
Step 2
Drain the potatoes and transfer to a bowl; add the sour cream and mash lightly; scrape into the bowl of a blender.
Step 3
Cut asparagus into 3 parts: woody ends tips and center pieces.
Step 4
Combine the woody ends of the asparagus with the vegetable broth in a stockpot; bring to a boil and cook until the woody ends are tender. Remove woody ends with a slotted spoon and discard.
Step 5
Remove 2 tablespoons broth to a bowl with the asparagus tips. Transfer remainder of stock to blender with the potatoes.
Step 6
Chop the middle segments of the asparagus.
Step 7
Heat olive oil in a skillet over low-heat; cook and stir the chopped asparagus chopped onion and 2 crushed cloves garlic in the hot oil until the asparagus is tender about 10 minutes. Add to the broth in the blender reserving oil in the skillet.
Step 8
Blend the mixture in the blender on high until smooth and creamy; return to the stockpot.
Step 9
Cook and stir the sliced mushrooms and 1 crushed garlic clove in the remaining oil over medium-low heat until the mushrooms soften 3 to 5 minutes. Add the white wine; cook another 1 to 2 minutes. Stir the mushroom mixture into the soup.
Step 9
Heat the asparagus tips and broth in the microwave for 2 minutes; stir into the soup.