Add the ham bone and 6 cups of water to a 4-quart Dutch oven. Put over high heat and bring to a boil, then reduce heat to a simmer and put the lid on. Simmer for 3 hours.

Slice the celery and carrots. Trim off the ends of the green beans and cut into bite sized pieces. Cut the potatoes into 1 to 2-inch cubes. Chop leftover ham into small cubes.

After the ham bone has simmered for 3 hours, remove it from the Dutch oven.

Add the veggies, potatoes, and ham into the broth and stir to combine. Turn the heat up to medium and cook for an additional 15 to 20 minutes or until the potatoes are soft when poked with a fork.

Add salt and pepper to taste.

Serve this soup with bread, toast, or just on its own.