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