In large sealable plastic bag, place olive oil, 3 tablespoons lime juice, lime zest, garlic, jalapeno and ginger. Add chicken and marinate in refrigerator at least 30 minutes.
Meanwhile, in medium saucepan over medium high heat, place coconut milk and chicken broth. Bring to a boil and add remaining 1/4 cup lime juice and salt. Stir in rice, cover, reduce heat and cook 30-50 minutes, until done.(You might start with the lowest amount of liquids, cooking time varies).
Remove chicken from marinade and discard marinade. Sprinkle chicken on both sides with jerk seasoning and place on broiler pan. Place under hot broiler about 8 inches from heat.
Cook about 8 minutes per side or until internal temperature reaches 165°F.
While chicken cooks, in medium skillet over medium high heat, place 2 tablespoons of the cooking oil. Peel plantains and cut in 1/2 inch thick slices. Fry in hot oil about 1-1/2 minutes per side, pushing down with back of spatula to flatten. When browned, remove from pan and drain on paper towels. Cut each slice into quarters, leaving a few whole for garnish.
Heat remaining 2 tablespoons oil in skillet. Add green onions and cook until soft. Stir in cooked rice, pineapple and soy sauce. Add chopped mint and cut plantains.
Place rice and chicken on serving dish, top with reserved fried plantains. Pour some of the Lime-Coconut Sauce over top and pass remainder in a small bowl. Garnish with lime slices, toasted coconut, red peppers, and mint sprigs. Enjoy!
Lime-Coconut Sauce: In small saucepan, place unsweetened coconut milk, brown sugar, grated lime zest, dark rum, fresh lime juice and kosher salt. Place over medium high heat and stir until hot.