Heat the butter and oil over low heat in a Dutch oven or large heavy-bottomed saucepan. Add the garlic and onions and cook, stirring frequently until the onions are soft and translucent, about 10 minutes.
Add the milk, 1 cup water, the rice, salt, marjoram, parsnips and cauliflower. Bring to a boil, and then reduce to a simmer, cover and cook until the cauliflower and parsnips are tender and the rice is thoroughly cooked, about 15 minutes. (Don't be alarmed if the milk looks curdled, it will become creamy once pureed.)
Working in batches, transfer the soup to a food processor and puree until smooth. For a thinner consistency, add more milk. Serve garnished with chives, if you like.