Pat the chicken dry, then rub all over with a paste made from 2 tbsp curry powder, allspice, garlic powder, onion powder, salt, black pepper, Scotch bonnet, half the garlic, soy sauce, and half the scallion. Cover and refrigerate for at least 30 minutes, or up to overnight.
Heat coconut oil in a large Dutch oven over medium heat, then add the remaining 1 tablespoon of curry powder and stir constantly for 1–2 minutes until the oil turns deep golden-orange and smells intensely fragrant.
Working in batches, place marinated chicken skin-side down in the pot and brown for 4–5 minutes per side without moving it, then transfer to a plate and repeat with remaining pieces.
In the same pot over medium heat, cook the diced onion for 4–5 minutes until softened, scraping up any browned bits, then stir in the remaining garlic, scallion, and fresh thyme sprigs for 1 minute until fragrant.
Pour in the chicken broth and water, stir in the brown sugar if using, then return all browned chicken pieces skin-side up to the pot. Bring to a boil, then reduce heat to low, partially cover, and simmer for 25 minutes.
Nestle the cubed potatoes and sliced carrots into the curry sauce around the chicken, replace the lid (slightly ajar), and continue simmering for 20–25 minutes until the potatoes are fork-tender and the chicken reaches 165°F (74°C).
Remove and discard the thyme sprigs, taste the sauce and adjust salt, heat, or sweetness as needed, then simmer uncovered for 5–10 minutes to thicken if desired. Serve hot over rice and peas or plain white rice.