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PREPARE THE CRUST::
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Preheat the oven to 375u00b0F.
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Line a baking sheet with parchment paper & wrap the outside of a 10-inch round springform pan with foil.
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In a medium bowl, toss the pecans with 1/2 teaspoon of the butter, 1/2 tablespoon of the granulated sugar, the brown sugar, the cream and salt.
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Spread the nuts on the prepared baking sheet and arrange them, right side up in a single layer.
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Bake for about 18 minutes, until the sugar is caramelized and the pecans are toasted; let cool.
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Transfer all but 12 of the pecans to a food processor.
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Add the graham crackers and pulse until finely ground.
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Add the remaining stick of melted butter and 1/3 cup of granulated sugar and pulse until the crumbs are moistened.
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Press the crumbs over the bottom of the pan and two-thirds of the way up the side of the prepared springform pan.
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PREPARE THE FILLING:.
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In a clean food processor, pulse the cream cheese with the sugar until smooth.
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Add the eggs, one at a time, and pulse until incorporated.
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Scrape down the side of the bowl.
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Pulse in the vanilla and sour cream.
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Scrape the batter into the pan and bake in the center of the oven for about 1 hour, until the top of the cheesecake is lightly golden in spots and the center is slightly jiggly.
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Transfer the cake to a rack and let cool completely.
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Wrap in plastic and refrigerate overnight.
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Unwrap the cheesecake and discard the foil.
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Remove the ring and transfer the cake to a plate.
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Arrange the 12 reserved pecans on top.
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Using a warm, slightly moistened knife, cut the cake into wedges, wiping and rewetting the blade between slices.
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Transfer the slices to plates and pour some of the Caramel Sauce on top.
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Serve with the remaining Caramel Sauce.
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*The cheesecake can be refrigerated for up to 5 days.
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PREPARE THE CARAMEL SAUCE:.
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In a medium saucepan, combine the butter with all three sugars and bring to a boil, stirring constantly.
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Cook over moderately high heat for 2 minutes, stirring constantly.
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Add the cream and boil for 2 minutes longer.
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Transfer the caramel sauce to a pitcher.
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Stir in the vanilla and salt and refrigerate until cold, at least 2 hours.
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**The caramel can be refrigerated for up to 1 week.
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Whisk to combine before serving.