Finely chop the garlic and onion.
Heat the oil in a saucepan, then sauté the onion and garlic for 5 minutes.
Meanwhile chop the broccoli. Remove and discard the woody parts of the asparagus, chop the rest.
When the onion is soft, add the broccoli and pour in the stock. Bring to the boil and simmer for 5/8 minutes, until the broccoli is tender. Add the asparagus and cook for another 3 minutes.
Turn off the heat and add the basil leaves. Using a stick blender, process the soup until you get a creamy texture.
Serve with freshly ground pepper and a dash of apple cider vinegar or lemon juice.