To make no-cream asparagus soup, prepare the asparagus. Cut the tips and keep aside. Chop up the rest of the asparagus, including the woody ends.
To a large pan, melt the butter under medium heat. Alternatively, heat the olive oil. Add the chopped onion, celery, and garlic. Saute till the onion becomes soft and translucent.
Add the potatoes, leek tops, and the asparagus. Mix well and cook for 5 minutes.
Add the vegetable stock. Check the salt and add as per taste. Cover the pan and let it simmer. Allow the vegetables to cook until they soften.
Meanwhile, prepare the celery tips. Add them to salted boiling water and let them simmer for 5 minutes till the tops soften. Alternatively, you can also steam them.
In a pan melt a teaspoon of butter or an equivalent amount of olive oil. Saute the asparagus tops in the butter/oil. Keep aside the tops.
Meanwhile, check if the soup vegetables have softened. Use an immersion blender to blend the vegetables into a smooth puree. Let the soup simmer for a couple of more minutes. Add pepper as per taste.
Serve the soup with asparagus toppings and croutons.