Preheat the oven to 400 degrees F. Line a baking sheet with aluminum foil. Cut off the tough ends of the asparagus and toss with 1 tablespoon olive oil and a sprinkle of salt. Roast the asparagus for 35 minutes. Chop coarsely and set aside.
Add the remaining tablespoon olive oil to a large dutch oven. Sweat the onions and celery over low heat with a pinch of salt until tender, approximately 5 minutes. Add the garlic clove and asparagus and continue cooking for another 5 minutes, stirring frequently.
Add the stock and thyme leaves. Bring the soup to a boil and then reduce to a simmer and cover the pot, leaving a small vent. Cook the soup for 45-60 minutes (the longer, the better).
Allow the soup to cool for 5-10 minutes and then ladle into a blender. Puree the soup until very smooth. The soup will have a bit of texture from the asparagus and can be pressed through a food mill if a smoother consistency is desired.
Return the soup to the dutch oven and stir in the cream and lemon juice. Season with salt and pepper to taste.
Serve soup in a small bowl with a dollop of crème fraîche and a sprinkling of chive blossoms (or regular chopped chives).