In a large Dutch oven, bring beans, ham hocks, and 8 cups water to a boil over medium-high heat. Reduce heat to medium-low to low; simmer, stirring occasionally and adjusting heat as needed, for 1½ hours. Discard ham hocks. Add broth and bay leaves.
Meanwhile, in a large skillet, heat oil over medium-high heat. Add chopped ham, bell pepper, celery, and onion, and cook, stirring frequently, until vegetables are tender, about 10 minutes. Add garlic, and cook, stirring constantly, for 1 minute.
Add ham mixture to bean mixture. Stir in mirliton, Creole seasoning, salt, oregano, and black pepper. Cook over medium-low heat until mirliton is tender, about 30 minutes. Discard bay leaves.
Add Parmesan in batches to soup, stirring constantly. (Don’t add all at once or it may clump.) Serve soup with bread. Garnish with rosemary, lemon zest, and Parmesan, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/mirliton-white-bean-and-ham-soup/