In a large bowl or gallon zip-lock bag, combine the onion, bell pepper, scallions, garlic, brown sugar, smoked paprika, allspice, ginger, and salt and pepper. Pat chicken pieces dry with paper towels, then add to the bowl along with the browning sauce. Massage all aromatics thoroughly into every piece of chicken until fully coated. Cover and refrigerate for at least 2 hours, or overnight for best results.

Remove chicken from the marinade and shake off excess vegetable bits. Set chicken aside on a clean plate. Reserve the marinade — do not discard.

Heat oil in a large dutch oven over medium-high heat until shimmering. Working in batches, sear chicken pieces on all sides for 2 to 3 minutes per side until a deep brown crust forms. Transfer to a clean plate and repeat with remaining pieces, adding more oil between batches as needed. Reduce heat to medium.

Add the reserved marinade mixture to the same pot. Saute for 2 to 3 minutes, scraping up caramelized bits from the bottom. Return all browned chicken to the pot with any collected juices. Add the carrots, tomato sauce, fresh thyme, bay leaves, whole scotch bonnet pepper, and chicken stock. Stir gently to combine.

Reduce heat to medium-low, cover the pot, and stew for 1 hour 30 minutes to 2 hours until chicken is completely tender and falling off the bone. Add a splash of stock if liquid reduces too quickly.

Discard thyme stems, bay leaves, and the whole scotch bonnet pepper. For a thicker gravy, raise heat to medium-high and simmer uncovered for a few minutes, stirring gently. Taste and adjust salt and pepper. Serve immediately over rice and peas with extra gravy spooned over the top.