Cook the 4 strips of bacon in a large pot over medium heat for 6 to 8 minutes until crisp; transfer to a plate. Melt the 4 tbsp butter into the reserved drippings, then cook the diced onion and 2 stalks diced celery for 5 to 6 minutes until softened. Add the 3 cloves minced garlic and cook for 60 seconds.

Stir in the 3 tbsp flour over the vegetables and cook for 90 seconds. Add the 3 cups chicken broth gradually, then the cubed potatoes, 1 tsp salt, 1/2 tsp black pepper, and 1/4 tsp smoked paprika. Bring to a boil, then simmer partially covered for 15 to 18 minutes until the potatoes are fork-tender.

Remove from heat and partially blend with an immersion blender using 8 to 10 short pulses, leaving chunks intact. Alternatively, blend 2 cups separately and stir back in.

Return to low heat. Stir in the 1 cup whole milk and 1/2 cup heavy cream and warm for 3 to 4 minutes without boiling. Remove from heat, then stir in the 1/2 cup sour cream and 3/4 cup of the shredded cheddar until melted and smooth.

Ladle into bowls and top each with the reserved 1/4 cup cheddar, crumbled bacon, and sliced chives.