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1. To make the crust, preheat the oven to 350u00b0F. Place the graham crackers in the work bowl of a food processor and process until finely ground. Combine the crumbs, butter, coconut, coconut extract, and salt in a medium-size mixing bowl and stir until moistened.
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2. Press the mixture evenly across the bottom and about 1 inch up the sides of a 9-inch springform pan, packing it tightly with your fingertips so it is even and compacted. Bake until crisp, 6 to 8 minutes. Let cool completely. (The crust may be wrapped in plastic wrap and frozen for up to 1 month.)
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3. To make the filling, place 1/2 cup of the cream of coconut in a small heatproof bowl, sprinkle the gelatin on top, and let soften for 5 minutes. Put 1 inch of water in a small saucepan and bring to a bare simmer. Place the bowl over the simmering water and heat, whisking constantly, just until the gelatin melts, 30 seconds to 1 minute.
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4. In a large bowl, using an electric mixer, beat the heavy cream until soft peaks form. Beat in the cream cheese and the remaining 1/2 cup cream of coconut until the mixture is almost smooth (a few small lumps are okay), 1 minute more. Stir in the coconut extract and vanilla extract. With the mixer running, pour in the liquefied gelatin. Continue to beat until the mixture is light and smooth, 2 to 3 minutes.
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5. Scrape the filling into the prepared crust, smoothing the top with a rubber spatula. Cover with plastic wrap and refrigerate until firm, at least 6 hours and up to 2 days.
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6. To make the sauce, push the mango puree through a fine-mesh strainer to remove any strings or tough fibers. Stir in the confectioners' sugar and rum. (You may refrigerate the sauce in an airtight container for up to 3 days.)
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7. Release the sides of the pan from the cheesecake. Drizzle Mango Sauce on dessert plates and then place a slice of cake over the sauce on each plate. Serve immediately.
