Brown the beef: Heat a large pot or Dutch oven over medium-high. Add the ground beef and cook, breaking it up with a spatula, until browned with crispy edges.
Season with a pinch of salt and pepper. Drain excess fat if needed, leaving about a tablespoon for flavor.
Sauté the aromatics: Add butter, onion, and celery to the pot. Cook 3–4 minutes until the onion is translucent and fragrant.
Stir in the minced garlic and cook 30 seconds more.
Add the cauliflower and spices: Toss in the cauliflower florets, smoked paprika, onion powder, garlic powder, and another pinch of salt and pepper. Stir to coat the vegetables in the seasonings and beef drippings.
Pour in broth and simmer: Add the beef broth and bring to a gentle boil. Reduce heat and simmer 10–12 minutes until the cauliflower is tender but not mushy.
Stir in cream and cheeses: Lower the heat to medium-low.
Add the heavy cream, cream cheese, and mustard. Stir slowly until the cream cheese melts and the soup looks creamy.
Melt the cheddar: Sprinkle in the shredded cheddar a handful at a time, stirring continuously so it melts smoothly. Avoid boiling at this stage to prevent separation.
Taste and adjust seasoning with salt and pepper.
Finish and serve: Let the soup gently simmer 2–3 minutes to thicken slightly. Ladle into bowls and top with chopped pickles, bacon, or green onions. Serve hot.