Sort and wash beans according to package directions. Place in a 3 1/2-quart or larger slow cooker. Fill the cooker with water to capacity. Soak without turning on the cooker, 8 hours to overnight.

Drain excess water and refill cooker with fresh water. Turn cooker to Low and cook until beans are soft, about 8 hours.

Heat oil in a large soup pot over medium-low heat. Add onions and carrots; cook, stirring occasionally, until onions are soft and carrots begin to soften, about 5 minutes. Add ham, tomatoes, and garlic and let simmer for another 5 minutes.

Puree about 2/3 of the cooked beans in small batches in a blender or food processor, using the bean broth to help puree and adding extra water if needed. Add puree and remaining whole beans to the soup pot; add enough water to bring soup to desired thickness. Stir in parsley, thyme, celery salt, salt, and pepper. Simmer slowly, stirring occasionally, until soup is hot and all vegetables are soft, about 20 minutes.