In a large pan, melt butter with oil over medium heat. Add onion and garlic and saute until softened, about 5 minutes. Add cauliflower and broth, season with salt and pepper and bring to a boil over high heat. Reduce heat to medium-low and simmer until cauliflower is very tender, about 20 minutes.

Remove from heat; let cool slightly. Working in batches, puree soup in a blender. Return soup to clean pot; stir in milk and mustard. Bring back to a simmer over medium heat. Add cheese and stir until cheese is melted (do not boil). Season with salt and pepper.

Ladle into bowls and sprinkle with additional cheese or croutons, if desired.