Place broccoli, onion, potato, carrots, chicken broth, water, cream of celery soup, salt, and pepper into a slow cooker. Stir gently to combine. Cover and cook on LOW for 6-8 hours or on HIGH for about 3 hours, until vegetables are very tender.
Use an immersion blender to puree a portion of the soup, leaving plenty of chunky vegetables for texture. If you don't have an immersion blender, transfer 1-2 cups of soup to a regular blender, puree until smooth, and return to the slow cooker.
Add the Velveeta and cheddar cheese to the slow cooker. If using ham, add it now as well. Stir gently, then cover and cook for another 15-20 minutes.
Stir again to make sure the cheese is completely melted and smooth. Taste and season with additional salt and pepper as needed.
Ladle into bowls and serve warm.