Cook the bacon in a large skillet over medium heat for 7–9 minutes, until crisp. Transfer to a paper towel-lined plate. Reserve 6 slices for the soup and 3 slices for topping.
Add the cubed potatoes, onion, garlic, chicken broth, salt, pepper, and thyme to a 6-quart slow cooker.
Cover and cook on LOW for 7–8 hours, until the potatoes are very tender.
Remove about 2 cups of potatoes and broth from the slow cooker. Mash until mostly smooth, then return the mixture to the slow cooker.
Add the softened cream cheese and half-and-half. Stir gently until the cream cheese begins to melt.
Add the shredded cheddar and crumble 6 cooked bacon slices into the soup. Cover and cook on HIGH for 20–30 minutes, stirring once or twice, until creamy and fully combined.
Stir and check the consistency. If the soup is too thick, add a small amount of warm chicken broth or milk.
Ladle into bowls and top with shredded cheddar, crumbled bacon, and sliced green onions.