In a 6- to 8-quart slow cooker, add the navy beans, garlic, sliced carrots,onion, potato, butter, salt, smoked paprika, and thyme. Pour in 8 cups of water and sprinkle generously with black pepper.
Set the slow cooker to high and cook for about 6 hours, or until the beans are soft and tender. Be sure the soup reaches a simmer during cooking to allow the beans to fully cook properly.
Once the soup is done, remove the ham hocks and set them aside to cool slightly on a cutting board.
Using a fork, mash the softened potato pieces against the side of the slow cooker for added creaminess. Stir well to break down some of the beans, enhancing the soup's texture.
Stir in the cider vinegar for a subtle tang, then shred the ham meat off the bones and return the meat to the slow cooker. Discard the bones.
Taste and adjust the seasoning with more salt or pepper, if needed, and serve hot.