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1. Preheat the oven to 400 F.
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2. In the bowl of a food processor, combine the flour, sugar, salt and coconut. Pulse until well combined. Add the cold butter and the shortening and pulse until you have a dough that will hold together. Transfer to a sheet of wax paper and form into a disc.
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3. Spray a 10 inch round tart shell with baking spray and then press the dough into the tart shell. Prick the bottom of the shell with a fork in several places.
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4. Bake the tart shell at 400 F for 18 minutes. At this point the tart shell will be lightly golden brown. Remove it from the oven and set it on a rack.
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5. While the tart shell is cooling, make the white chocolate ganache.
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6. Heat the 1/3 cup of whipping cream to a simmer in a small pot. Remove the pot from the heat and add the 1 cup of white chocolate chips. Whisk the cream and white chocolate until you have a smooth ganache. Pour the ganache into the bottom of the tart shell.
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7. Make sure the ganache is spread evenly around the bottom of the tart shell and then let it set up and cool completely, about 30 minutes.
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8. In a large bowl, combine the coconut cream, the heavy whipping cream and powdered sugar. Using an electric mixer, whip everything until you have a thick whipped coconut cream that holds a stiff peak.
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9. Empty the cream into the coconut tart shell and spread it evenly.
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10. Slice the fresh figs into quarters and arrange them in a concentric circle around the top of the tart. Keep refrigerated until you slice and serve.
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Note: The coconut cream for the filling is basically the solids from the top of a chilled can of coconut milk. But you can also buy entire cans of just the cream at Trader Joes.