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Special equipment: a 9-inch pie plate (preferably deep-dish) and pastry bag
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For the gingersnap cookie crust: Preheat the oven to 350 degrees F.
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Place the gingersnap crumbs in a large bowl and drizzle half of the melted butter all over.
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Using your hand or a silicone spatula, mix thoroughly.
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Add more butter a little at a time until you can make a fist with the crumbs that retains its shape but is easily broken (not too dry, and not too wet).
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Press the crumbs tightly into a 9-inch pie plate.
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A deep pie plate is much more suited to this task.
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Bake until the crust feels quite firm to the touch, 20 to 25 minutes.
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Set aside and let cool.
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For the pumpkin filling: Whisk together the milk, brown sugar and cornstarch in a saucepan and bring to a boil.
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Boil for 3 minutes, whisking constantly.
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In a large bowl, beat the eggs.
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Gradually add half of the hot milk mixture to the eggs, whisking constantly.
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Pour the mixture back into the saucepan and cook over medium heat, stirring often, until thick, about 3 minutes.
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Remove from the heat and whisk in the pumpkin puree and salt.
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Pour into the pie shell and chill until set, 2 to 3 hours.
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For the rum cheesecake topping: Cream together the cream cheese and sugar in the bowl of a stand mixer.
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Add the cream, rum extract, egg, nutmeg, cloves and vanilla bean seeds.
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Mix until well combined.
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Use a silicone spatula to fill a pastry piping bag with the filling.
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Cut off the tip.
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Pipe the cheesecake over the pumpkin filling, minding not to get too close to the crumb crust.
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Use a spatula to smooth out the topping to just meet the crust edge, being careful not to drag crumbs over the surface.
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Bake until the top is glossy and the center still wiggles, about 45 minutes.