In a large pot over medium heat, cook the chopped bacon until crispy. Scoop it out and set aside, leaving drippings in the pot.
Add onion and celery to the drippings and cook until soft. Stir in garlic and cook until fragrant.
Sprinkle flour over the vegetables and stir for about 2 minutes to form a roux.
Slowly stir in chicken broth. Add potatoes, salt, pepper, and ancho chili powder. Simmer until potatoes are tender.
Blend about half the soup using an immersion blender to create a creamy texture.
Stir in milk and heavy cream. Heat gently without boiling.
Ladle into bowls and top with shredded cheddar cheese, sour cream, crumbled bacon, and chopped chives.