Place beans in a large pot, cover with 2 inches of water. Bring to a boil. Remove from heat and cover, and let stand for 1 to 2 hours. Drain and rinse. Transfer beans to another container.
Heat oil in the large stockpot over medium-high heat. Add celery and onion and cook until translucent. Add ham bones, diced ham meat, beans, bouillon cube, and bay leaf. Cover with water or chicken stock. Reduce heat and simmer. Add additional water if needed until the stew is thickened, about 90 minutes.
Stir in cut carrots, salt, pepper, and parsley into the stew. Let simmer until the carrots are tender, about 30 minutes.
Garnish with more parsley and serve with Sweet Cornbread Cake