Prep the cauliflower: Rinse and cut the cauliflower into medium florets. Smaller pieces cook faster and blend smoother.
Sauté the aromatics: In a large pot, melt the butter over medium heat.
Add onion and cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds, just until fragrant.
Add cauliflower and broth: Toss in the florets, then pour in the broth. Add smoked paprika and ground mustard if using.
Bring to a boil, then reduce heat and simmer 12–15 minutes until cauliflower is very tender.
Blend to your preferred texture: Use an immersion blender directly in the pot for a smooth soup. For a chunkier texture, blend only half the soup and return it to the pot. A stand blender also works—just vent the lid and blend in batches.
Stir in cream: Return the pot to low heat and stir in the heavy cream.
Do not boil after adding cream—gentle heat keeps it silky.
Add the cheese: Remove the pot from heat and slowly whisk in the shredded cheddar by the handful until melted and smooth. If the soup is too hot, the cheese can separate, so keep it gentle.
Season to taste: Add salt, pepper, and red pepper flakes if you like a kick. Taste and adjust until it’s just right.
Garnish and serve: Ladle into bowls and top with crumbled bacon, extra cheddar, and chives or green onions.