Heat vegetable oil in a large pot over medium-high heat. Add the chicken pieces and brown on all sides. Remove the chicken and set aside.
In the same pot, add the chopped onion, garlic, and bell pepper. Cook until the onion is translucent, about 5 minutes.
Stir in the chopped tomatoes, thyme, paprika, allspice, ground black pepper, and salt. Cook for another 3-4 minutes.
Return the browned chicken to the pot. Add the rice, pigeon peas or kidney beans, coconut milk, chicken broth, soy sauce, and brown sugar. Stir to combine.
Place bay leaves and Scotch bonnet peppers (if using) on top of the mixture. Do not stir them in; they will infuse the dish with flavor.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for about 20-25 minutes, or until the rice is tender and the liquid is absorbed.
Remove the Scotch bonnet peppers and bay leaves before serving. Fluff the rice with a fork and serve hot.
Enjoy your meal!