Into a large skillet over medium high heat, add 2 cups broth and butter. Bring to a boil.
Reduce heat to low and add cabbage.
Cover and simmer 30 minutes, stirring occasionally, until cabbage is wilted. Season with salt and pepper, to taste. Remove from heat and set aside.
Into a large pot over medium heat, add the olive oil.
When oil is hot, add the onion, green pepper, red pepper, and celery. Cook, stirring frequently until vegetables are softened.
Stir in the remaining 2 cups of broth, rice, black-eyed peas, diced tomatoes, and garlic.
Bring to a boil, then reduce heat to low and simmer 30 minutes, or until the rice is done.
Add the cooked cabbage, with liquid, and continue cooking an additional 10 minutes, or until heated through.