Trim tips off of thawed asparagus spears; set aside.
Chop asparagus stalks and place in medium saucepan. Add chicken stock and bring to a boil over medium-high heat. Reduce heat and simmer for 8 minutes.
Transfer asparagus and stock to a blender and puree until smooth. Work in batches, if necessary. (TIP: To avoid spilling, cover blender with dish towel and pulse.)
Set mesh strainer over saucepan and pour asparagus puree into it, if desired, or return puree to saucepan. Add white sauce and whisk until smooth. Bring to a simmer over medium-high heat. Reduce heat to low and add cream and reserved asparagus tips. Heat soup through and adjust seasoning with salt and pepper.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.