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MAKE THE CAKE: Sprinkle 2 cups of the pecans evenly over the bottoms of 3 buttered 9" round cake pans, shaking to coat both the bottoms and sides of the pans.
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Combine the flour and baking soda in a bowl; mix well.
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In another bowl, using an electric mixer on medium speed, cream together the butter and shortening until light and fluffy.
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Gradually beat in the sugar.
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Add the egg yolks, one at a time, blending well after each addition; blend in the vanilla.
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Add the flour mixture and buttermilk alternately, blending well after each addition, beginning and ending with the flour mixture.
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Stir in the remaining 1 cup pecans.
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In a clean bowl, using an electric mixer with clean beaters on medium speed, beat the egg whites until stiff peaks form.
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Fold 1/3 of the whites into the batter to lighten it; fold in remaining whites.
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Pour batter evenly into the prepared pans.
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Bake at 350*F.
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for 25 minutes, or until a toothpick inserted in the center comes out clean.
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Cool 10 minutes in pans on wire racks; invert onto waxed paper-lined wire racks.
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Brush the tops and sides of the layers with the corn syrup; cool completely.
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MAKE THE FILLING: Whisk together the brown sugar, corn syrup, cornstarch, egg yolks, half-and-half, and salt in a heavy 3-quart saucepan until smooth.
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Bring to a boil over medium heat, whisking constantly; boil for 1 minute, or until the mixture thickens.
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Remove pan from heat; whisk in the butter and vanilla.
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Place a sheet of waxed paper on the surface of the mixture; chill for 4 hours.
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ASSEMBLE THE CAKE: Place 1 cake layer, pecan side up, on a serving dish; spread with 1/2 the filling.
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Place the second cake layer, pecan side up, over the filling; spread with the remaining filling.
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Place the third cake layer, pecan side up, on top of the filling.
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Serve with whipped cream; store covered in the refrigerator.
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Bring to room temperature before serving.