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Make this cake one day ahead.
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For crust: Wrap foil tightly around outside of a 9-inch round springform pan.
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In food processor, blend hazelnuts and sugar together until ground finely.
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Mix in the melted butter until it forms moist clumps.
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Press onto the bottom of the pan only. Do not coat the sides.
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For filling: Preheat oven to 350 F (325 F for dark pans).
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Using an electric mixer, beat the cream cheese, sugar and vanilla together in a large bowl until well mixed.
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Add the eggs one at a time, and beat just until well blended.
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Pour filling into the pan.
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Bake until cheesecake is puffy and the edges are set. The center should still wobble ever so slightly when gently shaking the pan, about 50 minutes.
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Set pan onto a wire rack, and run a sharp knife around the edges.
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Cool cake completely.
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Remove the foil. Cover the cake with plastic wrap and refrigerate overnight.
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For caramel sauce: Mix sugar and water in a heavy-duty medium saucepan. Heat over medium heat until the sugar is completely dissolved.
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Raise the heat to high, and boil without stirring until the syrup becomes a deep amber color. While heating, brush down the sides of the pan occasionally with a wet pastry brush. Also, occasionally swirl the pan. The whole process should take about 7 minutes.
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Remove from the heat and carefully add the cream (the mixture will bubble).
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Keep boiling until the sauce is reduced to 2 cups, stirring occasionally, about 5 minutes. Cool completely.
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Evenly distribute 1/2 cup of the caramel sauce on top of the cheesecake, leaving a 1/2-inch border from the edges.
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Place hazelnuts around the outside edges.
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Cover and chill until the topping is fully set, about 2 hours.
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(Can be prepared 1 day ahead, if you keep cheesecake covered and chilled. Refrigerate any remaining sauce.).
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To serve: Remove sides of pan, and transfer cake to serving plate.
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Rewarm remaining sauce just until pourable but not warm.
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Cut cheesecake into slices. Pass around the sauce separately.