In a 4-quart Dutch oven cook celery, onion, sweet pepper, and garlic in hot oil over medium heat for 5 minutes. Stir in ham, paprika, sugar; dry mustard; ground cumin; dried basil, crushed; dried oregano, crushed; and dried thyme, crushed. Cook and stir 5 minutes more.
Stir in black-eyed peas, hominy, undrained tomatoes, chicken broth, parsley, and molasses. Bring to boiling; reduce heat. Cover and simmer for 30 minutes. Makes 4 servings.