Coconut milk stands in for cream here, but this is not an Asian recipe.
Trim the tough ends of 1 bunch of asparagus. Cut the tips off the spears and reserve. Cut the stems into small pieces.
Clean and dice 1 leek and 3-4 stems of celery. Saute in 2 T. olive oil until tender and beginning to brown.
Add 2 minced cloves of garlic and 2 t. fresh thyme leaves plus salt and black pepper. Saute another 5 minutes.
Add 12 oz. coconut milk and 5 C. of vegetable stock, along with the asparagus and a bay leaf. Simmer for 10 minutes. Remove the bay leaf.
Transfer the soup in batches to a food processor or blender until it is completely pureed. Return to the pot and heat through, then taste and add lemon juice, salt and pepper.
Just before serving, quickly saute the asparagus tips in a little oil with salt, until just cooked. Float a few in each bowl when you serve the soup.