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Preheat an oven to 375 degrees F. Position a rack in the center of the oven.
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Position a second rack directly below it.
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FOR THE CRUST:.
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In a large bowl, combine the graham cracker and gingersnap crumbs, sugar, and ginger.
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Stir in the melted butter.
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Firmly press the crumbs into the bottom of a 9 1/2-inch springform pan.
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Brush the crust lightly with the egg white and chill for at least 15 minutes before filling and baking.
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FOR THE FILLING:.
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In a large bowl, beat together the cream cheese, sour cream, and brown and granulated sugars, using an electric mixer, until smooth.
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Gently beat in the egg yolks, then the pumpkin puree, vanilla, cornstarch, ginger, cinnamon, nutmeg, and cloves.
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In a large bowl, beat the egg whites, with a whisk or an electric mixer, until stiff peaks are formed.
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Fold the egg whites into the cream cheese mixture.
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Pour the filling into the prepared pan and place in the oven.
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Set an 8-inch-square baking pan filled halfway with hot water on the rack below the cheesecake (this helps prevent the top of the cheesecake from cracking).
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Bake until the center does not tremble when the cake is gently shaken, about 1 1/2 hours.
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Remove from the oven and allow to cool for several minutes.
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Place a rack 4 to 5 inches from the heat source of a broiler.
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Preheat the broiler.
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FOR THE TOPPING:.
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in a small bowl, combine the walnuts, ginger, and sugar.
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Add the butter and mix together with a fork or clean fingers until crumbly.
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Sprinkle over the warm cheesecake and place in the broiler to melt the sugar and caramelize the topping, 30 to 40 seconds.
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Watch carefully so that the topping does not burn.
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Remove the cheesecake from the broiler and let cool to room temperature.
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Cover and chill for at least 6 hours or as long as overnight.
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When it is chilled, run a knife around the edge of the cheesecake and remove the pan rim.
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Set the cheesecake on a serving plate without removing the pan bottom.
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Note: To toast walnuts, spread shelled nuts in a shallow pan.
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Toast in an oven preheated to 350 degrees F, stirring occasionally, until lightly browned, 8 to 10 minutes.