Heat the oil in a saucepan and gently fry the onion until softened but not coloured.
Add the rosemary and chopped asparagus and cook for 3-4 minutes. Allow to cool slightly.
Transfer the mixture to a blender and add the milk and parsley. Season, to taste, with salt and freshly ground black pepper and blend until smooth.
To serve, reheat the soup if necessary, then pour into a cappuccino cup and garnish with chives.