Cook the chopped bacon in a large pot over medium heat until crispy. Remove the bacon with a slotted spoon and set it aside, leaving the fat in the pot.

Add the diced onion to the pot and cook in the bacon fat until softened. Stir in the minced garlic and cook for one more minute.

Add the cubed potatoes and chicken broth to the pot. Bring the mixture to a boil, then reduce the heat and simmer until the potatoes are fork-tender.

Use a potato masher to break down some of the potatoes in the pot, leaving a few chunks for texture. Stir in the milk and heat through.

Remove the pot from the heat and stir in 1 cup of the shredded cheddar cheese until melted. Season with salt and black pepper.

Ladle the soup into bowls and top each serving with the reserved bacon, remaining cheddar cheese, and chopped chives.