In a large saucepan heat oil over medium heat. Add onion. Cook 5 to 7 minutes or until tender. Stir in flour, salt and pepper. Add broth all at once. Whisk to combine. Bring to a simmer, whisking occasionally. Whisk in cauliflower puree; simmer 5 minutes. Remove from heat and stir in cheese.
Cool mixture slightly. In a blender, blend mixture, half at a time, until smooth.
Ladle soup into bowls.
Steam cauliflower florets until tender, about 14 minutes. Puree in a food processor with half and half, and salt and pepper to taste. Freeze half.