Place the cubed potatoes, diced onion, minced garlic, chicken broth, salt, and black pepper into the slow cooker. Stir once to combine.
Cover and cook on low for 7 hours until the potatoes are very soft.
Use a potato masher to break down some of the potatoes right in the slow cooker for a thicker texture. Leave some chunks for body.
Stir in the milk and 1/2 cup of the shredded cheddar cheese until the cheese melts and the soup looks creamy.
While the soup finishes, cook the bacon in a skillet over medium heat until crisp. Drain on paper towels and crumble into small pieces.
Ladle the soup into bowls. Top each serving with the remaining shredded cheddar cheese, crumbled bacon, and chopped chives.