Heat the oil in a non-stick pan, add the onions and sauté till they turn translucent.
Add the potatoes and vegetable stock and bring to boil. Cover and cook over a slow flame till the potatoes are cooked.
Add the asparagus and cook for a few more minutes.
Cool the mixture and grind to a smooth purée in a blender.
Pour the purée back into the pan, add the milk, salt and pepper and simmer for a few minutes.
Add a little water if required to adjust the consistency of the soup.
Serve hot sprinkled with freshly ground pepper.
VARIATION: PARSLEY SOUP
Substitute the asparagus with 1 cup of chopped parsley.