Bring a large pot of water to a boil. Fill a medium bowl with salted ice water. Working in 2 batches, add the asparagus to the boiling water and cook until just tender, about 4 minutes per batch. Using a slotted spoon, transfer the asparagus to the bowl of ice water. Drain. Reserve 7 1/2 cups of the cooking liquid.
Thinly slice 18 of the asparagus tips on the diagonal and reserve for a garnishing the soup. Chop the remaining asparagus spears into small pieces.
Melt the butter in a large pot over medium heat. Add the onion, celery, and carrots and cook, covered, stirring occasionally, until soft, about 12 minutes. Add the flour and cook, stirring with a wooden spoon, for 2 minutes more.
Pour in the reserved asparagus cooking liquid and bring to a boil while whisking constantly. Tie the parsley, thyme, and bay leaf together with a piece of kitchen twine and add to the soup. Lower the heat, and simmer for 10 minutes.
Stir in the chopped asparagus and bring to a boil. Remove from the heat and allow to cool.
Remove and discard the herb bundle. Working in batches, transfer the asparagus mixture to a blender and puree until smooth. Using a sieve over a large bowl, strain the asparagus soup. Return the puree to the pot and reheat over medium heat.
Whisk the heavy cream, vermouth, and salt into the soup and season with pepper. Divide among warm soup bowls, sprinkle each soup with the reserved asparagus tips, and serve immediately.
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