Sauté the aromatics. In a large pot or Dutch oven over medium heat, warm 1 tablespoon butter or oil. Add the chopped onion and a pinch of salt. Cook 3–4 minutes until softened.
Stir in garlic for 30 seconds until fragrant.
Brown the beef. Add ground beef, breaking it up with a spoon. Season with salt, pepper, and smoked paprika. Cook until browned and no longer pink, about 6–8 minutes.
If needed, drain excess fat, leaving a bit for flavor.
Add cauliflower and broth. Stir in cauliflower florets, beef broth, tomato paste, and a small pinch of chili powder if you like heat. Bring to a simmer and cook 10–12 minutes until the cauliflower is tender.
Make it creamy. Reduce heat to low. Stir in cream cheese until fully melted and smooth.
Slowly pour in heavy cream, stirring constantly to prevent curdling. Do not boil once dairy is added.
Stir in cheese and burger extras. Add shredded cheddar, mustard, chopped dill pickles, and a teaspoon or two of pickle juice. Stir until the cheese melts and the soup thickens slightly.
Taste and adjust salt and pepper.
Finish and serve. Let the soup sit over low heat for 2–3 minutes to marry flavors. Ladle into bowls and top with bacon, more cheddar, or scallions if you like.