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1.
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For crust, combine crumbs and 2 tablespoons sugar.
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Stir in butter, toss gently.
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Press onto bottom and 1 inch up sides of a 9-inch springform pan.
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Bake in 375 degree F oven about 10 minutes or until edges begin to brown.
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Cool slightly on a wire rack.
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2.
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Meanwhile, for filling, combine cream cheese, 1 cup sugar, cinnamon, and apple-pie spice.
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Beat until fluffy.
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Beat in applesauce and lemon juice.
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Beat in eggs until combined.
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3.
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Pour filling into crust-lined pan.
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Bake on a shallow baking pan in a 375 degree F oven 40 to 45 minutes or until center is nearly set.
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Cool on a wire rack 15 minutes.
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Loosen sides of pan.
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Cool 30 minutes more; remove sides.
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Cool completely.
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Chill at least 4 or up to 24 hours.
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4.
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For sauce, in a small heavy saucepan melt 1/2 cup sugar over medium-high heat until sugar begins to melt, shaking pan often.
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(Do not stir.)
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Reduce heat; cook about 5 miutes more or until sugar is melted and golden.
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Stir as necessary after sugar begins to melt (only when mixture bubbles).
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Remove from heat.
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Carefully pour in 1/2 cup whipping cream.
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Add 1 tablespoon butter.
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Return to heat; cook and stir for 1 to 2 minutes more or until smooth.
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Stir in 1/3 cup coarsely chopped pecans.
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Cool.
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Cover and chill up to 24 hours.
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To serve, cut cheesecake into wedges; top with sauce.