Set a large pot over medium heat and add the olive oil. When the oil is hot, add the onion, green pepper, red pepper, and celery. Cook, stirring frequently, until the vegetables are crisp-tender, about 5 minutes.
Add the broth, brown rice, black-eyed peas with their liquid, diced tomatoes with their liquid, and garlic. Stir to combine. Bring to a boil, then reduce the heat to low.
Simmer uncovered for 45 minutes, stirring occasionally, until the rice is cooked through and the broth has thickened slightly.
Stir in the pre-cooked cabbage and continue cooking for an additional 15 minutes. Adjust seasoning to taste and serve hot.