Into a large pot over medium heat, add the olive oil.
When the oil is hot, add the onion, green pepper, red pepper, and celery.
Cook, stirring frequently until vegetables are crisp-tender.
Add the broth, rice, black-eyed peas with liquid, tomatoes with liquid, and garlic.
Bring to a boil, then reduce heat to low.
Simmer, uncovered, for 45 minutes.
Add the pre-cooked cabbage.
Continue cooking an additional 15 minutes.