Heat oil in a large pot over medium heat. Add onions and garlic. Cook and stir until onions begin to soften about 3 minutes.
Stir in cauliflower, sweet potato, curry and cumin. Cook and stir for 1 more minute. Add broth, salt and pepper. Bring mixture to a boil. Reduce heat to low, cover and simmer for 12 to 15 minutes, until vegetables soften.
Roughly puree the soup using a potato masher. Stir in cooked rice, milk and cheese. Heat soup 1 more minute until cheese melts. Serve hot with crusty bread or naan bread.