Preheat the oven to 400°F. Pierce the potatoes several times with a fork and bake them for 45 to 60 minutes until tender. Let them cool slightly, then scoop out the flesh and set it aside.
Cook the bacon in a large pot over medium heat until crisp. Remove the bacon with a slotted spoon, drain it on paper towels, and crumble it once cool. Leave 1 tablespoon of bacon fat in the pot.
Add the butter to the pot along with the diced onion. Cook for 5 minutes until the onion softens. Stir in the minced garlic and cook for 1 minute more.
Pour in the chicken broth and add the baked potato flesh. Bring the mixture to a simmer and cook for 10 minutes, stirring occasionally.
Use a potato masher to break down the potatoes until the soup reaches a chunky yet creamy consistency. Stir in the milk and shredded cheddar cheese until the cheese melts.
Season with salt and black pepper. Ladle the soup into bowls and top each serving with the crumbled bacon and chopped chives.