Pat fish dry. Rub with lime juice, salt, black pepper, all-purpose seasoning, allspice, and browning sauce. Rest 15 minutes.
Dust fish lightly with flour, shaking off any extra.
Heat oil in a large skillet over medium-high. Sear fish until golden, 2–3 minutes per side. Transfer to a plate.
Reduce heat to medium. Sauté onion, carrot, and bell pepper in the same pan until softened, about 4 minutes.
Stir in garlic, thyme, scallions, and Scotch bonnet. Cook 1 minute until fragrant.
Add tomatoes, ketchup, soy sauce, and brown sugar. Pour in broth and bring to a lively simmer.
Nestle fish into the sauce. Spoon sauce over the top, cover, and simmer gently 8–10 minutes until the fish flakes.
Adjust salt to taste. Sprinkle with parsley and serve hot.