1. Cook the chopped bacon in a large pot over medium heat until crisp, then transfer it to a paper towel-lined plate and keep about 2 tablespoons of drippings in the pot.

2. Add the butter, onion, and carrots to the pot, then cook for 4 to 5 minutes until softened.

3. Stir in the garlic and cook for 30 seconds until fragrant.

4. Sprinkle in the flour and stir constantly for 1 to 2 minutes to form a roux.

5. Slowly pour in the chicken broth while stirring, then add the milk, heavy cream, Dijon mustard, smoked paprika, salt, and black pepper.

6. Add the broccoli and bring the soup to a gentle simmer, then cook for 12 to 15 minutes until the broccoli is tender.

7. Blend about one-third of the soup with an immersion blender for a thicker texture while leaving plenty of broccoli pieces whole.

8. Reduce the heat to low and stir in the shredded cheddar cheese a handful at a time until melted and smooth.

9. Stir in half of the cooked bacon, then taste and adjust the seasoning.

10. Serve hot with the remaining bacon, extra cheddar, parsley, and black pepper on top.