Add the potatoes, onion, chicken broth, garlic, butter, salt, and pepper to the slow cooker. Cover and cook on High for 4 hours or on Low for 8 hours, until the potatoes are very tender.
Mash the mixture until the potatoes are mostly broken down and the soup begins to thicken, leaving a few small chunks if desired.
Stir in the heavy cream, shredded cheddar cheese, and chives until the cheese is melted and the soup is creamy.
Serve warm and top with sour cream if using, bacon, extra cheese, and chives.