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Place the chicken in a sealable plastic bag. Whisk together the lime juice and the 1 tablespoon of curry powder, and then pour into the plastic bag. Massage the curry lime juice into the chicken, and then seal the bag and place it in a bowl in the refrigerator. Let chill and marinate overnight.
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Heat a large Dutch oven over medium high heat. Pat the chicken pieces dry and sprinkle with salt and pepper. Add the coconut oil to the pot--when it is melted and shimmering, brown the chicken in batches. Set aside.
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Add the butternut squash and potatoes into the hot Dutch oven. Sprinkle with salt, let fry undisturbed for 2-3 minutes, then toss, salt and repeat. Do this 3 times.
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Sprinkle the allspice, 1 tablespoon curry powder, garlic and ginger into the Dutch oven. Toss. Add the bell pepper and white and light scallion parts and toss again. Cook for 2 minutes.
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Add the lime zest, 4-6 thyme sprigs (use less for longer sprigs, more for shorter) and the coconut milk. Toss in the browned chicken, along with any accumulated juices, and bring to a boil. Reduce the heat to maintain a gentle simmer and cover the pot. While the chicken is braising, prepare the love apples.
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In a separate nonstick skillet, heat 1 tablespoon of coconut oil. When it is melted and shimmering, add the tomatoes. Cook, stirring occasionally, for 5 minutes and let juices evaporate. Then add the brown sugar and let the tomatoes caramelize in the sugar for another 2-3 minutes.
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When the chicken has cooked through, probably about 15-20 minutes, add the caramelized tomatoes to the stew. Then add the rum and the juice of half a lime. Taste for more salt or lime juice. Add the 1 tablespoon brown sugar if needed.
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Serve sprinkled with thyme leaves and the green parts of the scallions.