Asparagus stock: Wash the asparagus and snap off the woody ends. Place them in a soup pot, add the water, sugar, 1 teaspoon butter, and salt and bring to a boil. Turn down the heat and simmer, uncovered, for 20 minutes. Remove the asparagus woody ends with a slotted spoon and discard (Notes 1,2).
Cook soup: Add the chopped asparagus stalks to the stock. Save the asparagus tips for finishing the soup. Simmer the asparagus stalks in the soup, covered, for 20 minutes or until soft. Drain and reserve the stock.
Make the roux: Wipe the pot clean. Melt the butter and cook the finely chopped onion for about 3 minutes until golden, but not brown. Sprinkle the flour in the pot and stir for 1 minute. Slowly and gradually add the stock while whisking all the time. Bring to a boil and simmer for about 3 minutes until thickened.
Add the cooked asparagus, coriander, lemon juice, and milk. Add some salt and pepper as well. Bring to a boil again and simmer for about 5 minutes.
Blend the soup until creamy.
Add the asparagus tips, bring to a boil again and simmer for another 2-3 minutes. The asparagus tips should not get too soft. Adjust the taste with salt and pepper.