Marinate the chicken: In a large bowl, combine the chicken pieces, all-purpose-seasoning or bouillon powder, 1 tablespoon of Jamaican curry powder, chopped onion, minced garlic, grated ginger, chopped Scotch bonnet pepper, thyme leaves, 1/2 teaspoon of allspice, salt, and black pepper. Mix well, ensuring that the chicken is well coated with the spices. Cover and refrigerate for at least 2 hours, or overnight for best results. Brown the chicken: In a large, heavy-bottomed pot or Dutch oven, heat the vegetable oil over medium heat. Add the remaining 1 tablespoon of Jamaican curry powder and cook for about 1 minute, until fragrant. Add the marinated chicken pieces to the pot, and cook for 5-7 minutes, turning occasionally, until the chicken is browned on all sides.
Add liquid and vegetables: Pour in the chicken broth, making sure to scrape up any browned bits from the bottom of the pot. Add the cubed potatoes and chopped carrot, and stir to combine. Bring the mixture to a boil, then reduce the heat to a simmer.
Simmer the curry: Cover the pot and let the curry simmer for about 40 minutes, or until the chicken is cooked through and the vegetables are tender. If the curry needs more liquid, add a bit more chicken broth or water.
Finish and serve: Stir in the coconut milk, and let the curry cook for another 5 minutes to let the flavors meld. Taste and adjust the seasoning if necessary. Remove from heat and garnish with sliced green onions and fresh cilantro or parsley, if desired. Serve the Jamaican curry chicken over steamed white rice or with roti bread.