Cook the bacon: In a large pot or Dutch oven over medium heat, cook chopped bacon until crispy, 6–8 minutes.
Transfer bacon to a paper towel–lined plate. Leave 1–2 tablespoons of bacon fat in the pot and discard the rest.
Sauté aromatics: Add butter to the pot with the bacon fat. Stir in onion and cook until softened and translucent, about 4–5 minutes.
Add garlic and cook 30 seconds, until fragrant.
Add cauliflower and spices: Toss in the cauliflower florets, smoked paprika, black pepper, and a pinch of salt. Stir to coat the cauliflower in the buttery aromatics.
Simmer: Pour in the chicken broth. Bring to a boil, then reduce to a gentle simmer.
Cover and cook 12–15 minutes, or until the cauliflower is very tender when pierced with a fork.
Blend: Turn off the heat. Use an immersion blender to puree the soup until smooth and creamy. For extra silky texture, blend in batches in a countertop blender, venting the lid and covering loosely with a towel.
Return to the pot.
Make it creamy: Stir in heavy cream and 1 cup of the shredded cheddar. Add red pepper flakes if using. Warm over low heat until the cheese melts and the soup is steamy, 2–3 minutes.
Do not boil.
Finish and season: Whisk in sour cream. Taste and adjust salt and pepper as needed. If the soup is too thick, thin with a splash more broth or cream.
If too thin, simmer gently a few extra minutes.
Serve loaded-style: Ladle into bowls and top with crispy bacon, remaining cheddar, extra sour cream, and chopped chives or green onions.