Rinse and sort the navy beans, discarding any debris.
Place beans in the slow cooker. Nestle in the ham bone or hock.
Scatter diced ham, onion, carrots, celery, and garlic over the beans.
Sprinkle in thyme, smoked paprika, pepper, and salt. Pour in broth and water.
Stir gently to combine. Cover and cook on Low for about 8 hours.
Remove the ham bone. Shred any meat, discarding bone and excess fat.
Return shredded ham to the pot. Stir in the apple cider vinegar.
Taste and adjust seasoning. Let stand 10 minutes to thicken, then serve warm.