Trim the top tips from the asparagus,about 1 to 1 1/2 inches inn length. Cut the woody stem ends from each spear and reserve. Cut the remaining tender stalks into 1/2 - inch pieces.
In a medium pot , bring stock to a boil . Add the tough woody stems, lower the heat and simmer to infuse with asparagus flavor , 30 minutes. Remove with a slotted spoon and discard, reserving the stock .
Add the top tip of the asparagus to the stock and blanch until tender , 2 minutes . Remove with a strainer and refresh in an ice water bath. Drain on paper towels and reserve the garnish. Reserve the stock.
In a medium pan , melt the butter over medium high heat . When foamy add the onions and leeks and cook until tender , about 3 minutes . Add the garlic and the chili paste and cook until fragrant, about 1 minute. Add the chopped asparagus stalks, salt and pepper , and cook, stirring for 2 minutes . Add the reserved broth and simmer until the asparagus is very tender, 20 minutes. Remove from the heat.
With a hand -immersion blender or in batches in a food processor, puree the soup until smooth . Return to medium high heat and add the cream and reserved asparagus tips . Cook until soup is warmed through , about 3 minutes .