In a large bowl, combine chicken, brown sugar, smoked paprika, allspice, black pepper, salt, chopped onions, green onions, red bell pepper, garlic, and ginger. Mix well to coat the chicken evenly.
Cover and marinate in the refrigerator for at least 1 hour, or overnight for best flavor.
Heat oil in a large skillet over medium heat. Remove chicken from the marinade, reserving the vegetables and spices, and brown the chicken on both sides, about 3-4 minutes per side.
Remove the chicken and set aside. In the same skillet, add the reserved vegetables and spices from the marinade and sauté until softened, about 5 minutes.
Return the chicken to the skillet. Add ketchup and chicken broth, and stir to combine. Bring to a simmer.
Cover and cook on low heat for 45 minutes.
Uncover and cook for an additional 15 minutes to reduce the sauce slightly. If using, add the Scotch bonnet pepper during the last 15 minutes of cooking.
Serve hot with rice or your choice of side.