Heat the oil in a non-stick pan
Add the onions and saute 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 puree in a blender
Pour the puree 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