Slice the leek, including the green part. Peel the potatoes then cut them into cubes. Chop the broccoli stalk into chunks and tear the florets apart.
Heat the oil in a pan, then then gently sauté the leek for 5 minutes, then add the garlic and cook for another 3 minutes. Add the potatoes and broccoli stalk pieces. Sauté (under cover) for another 5 minutes, then add the stock and broccoli florets.
Bring to the boil and cook for about 15 minutes, until the vegetables are tender.
Turn off the heat. Add the parsley leaves and, using a stick blender, purée the soup until smooth and silky.
Serve it with freshly ground pepper and a small spoonful of apple cider vinegar.