Cook the Bacon: Fry ½ pound bacon in a large pot until crispy; remove and set aside, leaving 3–4 tablespoons of bacon grease in the pot.
Sauté the Vegetables: Add 1 chopped onion, 2 chopped celery stalks, and 2 minced garlic cloves to the bacon grease; cook 5–7 minutes until onions are soft.
Make the Roux: Add 2 tablespoons butter to the pot; once melted, whisk in 2 tablespoons flour and cook 1–2 minutes, stirring constantly.
Add Potatoes and Stock: Add 5–6 peeled and diced potatoes, pour in 4–5 cups chicken stock until potatoes are covered, bring to a boil, then simmer 15–20 minutes until tender.
Blend for Creamy Texture: Blend about half the soup with an immersion blender or in a regular blender; return to pot and stir.
Add Cream and Season: Stir in 1 cup heavy cream and warm over low heat; season with salt and black pepper to taste.
Serve and Top: Ladle soup into bowls and top with crumbled bacon, 1 cup shredded cheddar cheese, and chopped chives.