Rinse and sort through the beans, discarding any rocks or debris. Set aside. Reserve seasoning packet for later.
Dice the onion and celery. Peel and shred or finely dice the carrots. Mince the garlic.
Add the oil to a large stock pot over medium heat. When hot, stir in the onion, celery, and carrot.
Cook vegetables until softened, about 5 minutes. Stir in the garlic and cook 30 more seconds.
Add the chicken broth to the pot along with the dried beans.
Bring to a boil over medium heat, reduce to a simmer, and cover with a lid. Cook for 2 hours or until beans are mostly tender.
Add the ham, salt, pepper, and reserved seasoning packet to the soup. Continue simmering for 30 minutes to an hour more, or until beans are tender. Add additional broth as desired.