Cook bacon pieces in a large Dutch oven or soup pot over medium heat until they are crisp and browned.

Remove the cooked bacon and set aside, leaving the rendered fat in the pot; then add butter and chopped onion and cook until tender for 3-5 minutes.

Add minced garlic and cook for about 30 seconds until fragrant, then sprinkle flour over the ingredients and stir until smooth, using a whisk if needed.

Stir diced potatoes into the pot along with chicken broth, milk, heavy cream, salt, pepper, and ancho chili powder, mixing everything well.

Bring the soup to a boil and cook for approximately 10 minutes, or until the potatoes are tender when pierced with a fork.

Reduce heat to a simmer, then carefully transfer about half of the soup (roughly 5 cups) to a blender and puree until smooth; alternatively, use an immersion blender.

Return the pureed soup to the pot, then add the sour cream and the reserved cooked bacon pieces, stirring well to combine.

Allow the soup to simmer for 15 minutes before serving, and top with additional sour cream, bacon, cheddar cheese, or chives if desired.