Peel and core the pineapple, reserve the core. Cut the pineapple into about 1 1/2-inch chunks and roughly chop the core. Set the pineapple chunks aside.
In a medium bowl, combine the pineapple core, 3/4 cup of water, allspice, ginger, cinnamon, and star anise. Set aside.
In a medium saucepan, stir together the sugar, corn syrup, and just enough water so that it resembles wet sand. Place the pan over medium to medium-high heat and cook, stirring, until the mixture begins to boil. Stop stirring and continue to cook until golden brown, about 5 minutes. Remove the pan from the heat and carefully add in the spice mixture. Stir the caramel, return it to medium heat, and simmer until reduced to a glaze, about 8 minutes. Set the caramel aside and let cool slightly. Strain the caramel into a bowl and discard the solids.
Add the pineapple chunks to the caramel and toss to combine. Marinate at room temperature for an hour or refrigerate overnight.
Put the toasted coconut on a plate. Using a fork, remove the pineapple chunks from the caramel. Working with one chunk at a time, roll the pineapple in the coconut, pressing it on. Thread the coconut-coated pineapple chunks onto the ends of the skewers, about 1 or 2 per skewer. Transfer to a serving platter and strew the mint over the top. Serve at room temperature.
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