In a large bowl, combine chicken pieces with curry powder, allspice, garlic powder, onion powder, salt, and black pepper. Mix well to coat the chicken evenly. Let it marinate for at least 30 minutes, or up to overnight in the refrigerator for more flavor.
Heat vegetable oil in a large pot or Dutch oven over medium heat. Add the marinated chicken and brown on all sides, about 5-7 minutes. Remove the chicken and set aside.
In the same pot, add chopped onion, garlic, ginger, and bell pepper. Sauté until the vegetables are softened, about 3-4 minutes.
Return the browned chicken to the pot. Pour in the chicken broth and coconut milk, stirring to combine.
Add sliced carrots and bring the mixture to a simmer. Cover and cook on low heat for 30-40 minutes, stirring occasionally, until the chicken is cooked through and tender.
Taste and adjust seasoning if necessary. Garnish with chopped green onions and cilantro before serving.