Cut the florets off the broccoli head and peel the stalk, trying not to waste any of the broccoli; dice the stalk.
In a large saucepan saute the onion in the vegetable oil until soft. Add the potatoes, broccoli, vegetable stock, salt, pepper and parsley then cover with the saucepan lid and simmer until potatoes and broccoli are soft.
Allow to cool slightly and blend until soup is smooth. Add the cream and stir.
Soup may need to be reheated slightly before serving.