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Preheat the oven to 375°F. Spray 16 muffin cups with nonstick cooking spray or line them with cupcake liners. (See Café Tips above in the post about alternatives.)
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If your raisins look dried out, place them in a small bowl and cover them with hot water. Set aside for 5 minutes then drain well.
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In a large bowl, combine the flour, brown sugar, baking soda, spices, and salt. Stir well.
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Add the carrots, raisins and coconut and stir to combine. Run your hands through the mixture, breaking up any small clumps of brown sugar, coconut or raisins that remain. Make a well in the center of the mixture then set it aside.
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In a separate bowl, whisk together the eggs, oil, pineapple, pineapple juice and vanilla until well combined.
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Add egg mixture to the well in the flour mixture. Stir just until all of the flour is incorporated (mixture will be quite thick). Divide the batter among the cups of the prepared pans, filling almost to the top (about ⅞ full). Sprinkle each muffin with about ½ teaspoon of Demerara sugar. Place the muffins in the oven and immediately reduce the temperature to 350˚F.
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Bake the muffins for 22 to 28 minutes, until they're nicely domed and a cake tester inserted in the center comes out clean. Remove from the oven, cool for 5 minutes in the pan, then remove from pans and cool on a wire rack.