In a large pot, heat the vegetable oil over medium heat. Add the finely chopped onion, bell pepper, and minced garlic. Sauté until the vegetables are soft and the onion is translucent, about 5 minutes.
Stir in the tomato paste, thyme, paprika, ground allspice, and bay leaf. Cook for another 2-3 minutes, allowing the spices to become fragrant.
Add the rinsed rice to the pot, stirring to coat the grains with the tomato and spice mixture. Then, add the cooked and drained pigeon peas (or black-eyed peas).
Pour in the chicken or vegetable broth and season with salt and pepper to taste. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and simmer for about 20-25 minutes, or until the rice is tender and the liquid is absorbed.
Remove the pot from the heat and let it sit, covered, for about 5 minutes. Fluff the rice with a fork and remove the bay leaf before serving.
Enjoy your meal!