Preheat oven to 400 degrees F. Beat the eggs until well combined and light in color, about 5 minutes. Mix the sugar and flour together and gradually add to the eggs using low speed. Add the corn syrup, vanilla and salt and blend well, again using low speed. Fold the nuts in by hand and pour the mixture into the prepared pie crusts. Bake at 400 degrees F for 10 minutes and then reduce the heat to 350 degrees F. and bake for 1 hour longer. The pie will rise up and form cracks on the top, and the filling will be set when baking is complete. Remove pie and let it cool before cutting.
Combine the butter, shortening, 2 cups of the cake flour, and 1 cup of the all-purpose flour. Blend together. Stop mixer, scrape the sides and add remaining 2 cups of cake flour and remaining 1 cup of all-purpose flour. Blend to combine completely. Mix sugar and salt into 1/4 cup of the water and add it to the flour mixture. Blend briefly and add the remaining water if needed. The dough should not be overworked and should make a solid piece when held in your hand. Turn the dough out onto a lightly floured smooth surface and knead it several times. Divide the dough into portions and flatten it. Wrap unused dough in plastic. Roll out the dough to fit a 9-inch pie pan. Re-roll any scraps for a second pie crust.
Preheat oven to 475 degrees F. Prick bottom and sides of pastry with fork. Bake 12 minutes or until light brown. Cool on wire rack.