Add the butter to large, deep heavy bottomed pot over low heat and let melt. Add the onion and garlic to the pot and cook, stirring often, for 5 minutes to soften.
Add the cauliflower, salt, mustard powder, red pepper flakes, and chicken broth to the pot and increase heat to medium.
Bring to a boil and reduce to a simmer, stirring occasionally. Simmer for 15 minutes.
Use an immersion blender to blend the soup until smooth and creamy. Alternately, carefully transfer the hot soup to a blender and blend. Add the cream and cheddar to the soup and stir well to combine.
When the cheese has fully melted, add the broccoli to the soup and cook for 5-10 minutes or until broccoli is as soft as you'd like, stirring occasionally. Serve with additional grated cheddar and crumbled bacon, if desired.
