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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.
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2
Drain the potatoes and transfer to a bowl; add the sour cream and mash lightly; scrape into the bowl of a blender.
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3
Cut asparagus into 3 parts: woody ends, tips, and center pieces.
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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.
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5
Remove 2 tablespoons broth to a bowl with the asparagus tips. Transfer remainder of stock to blender with the potatoes.
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6
Chop the middle segments of the asparagus.
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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.
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8
Blend the mixture in the blender on high until smooth and creamy; return to the stockpot.
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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.
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10
Heat the asparagus tips and broth in the microwave for 2 minutes; stir into the soup.
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11
Season the soup with cayenne pepper, salt, and black pepper.
