Heat oil in a pot over medium heat, and then add asparagus and onion and cook, stirring, 4 to 5 minutes.
Mix in flour, and then stir in stock.
Bring to a simmer and cook until asparagus is very tender, about 20 minutes. Pure mixture in a food processor or blender, and then return to the pot. Add remaining ingredients, bring back to a gentle simmer, and then serve. Garnish soup and serve.