Heat the oil in a large saucepan, and add the onion and garlic. Cook over a medium-low heat for 5 minutes, until soft.
Add the chopped cauliflower and diced potato, along with the vegetable stock, water, dried parsley, and plenty of black pepper. Bring to a simmer, and cook for around 15-20 minutes, until the vegetables are very soft.
Turn the heat down low, and use an immersion blender to blend the soup until smooth.
Add the grated cheddar (save a little back for garnish, if you like), and mix until the cheese has melted. Serve warm, topped with any remaining cheese, and some homemade croutons and fresh parsley if desired.