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Preheat the oven to 350 degrees F.
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Grease and flour two 8-inch round cake pans.
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Cream the shortening with the 1 cup sugar.
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Add 1 egg and beat until blended.
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Sift the 1-3/4 cups flour together with the baking powder and 1/8 teaspoon salt.
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Add to the creamed mixture alternately with the milk.
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Stir in the vanilla. Divide the batter between the cake tins.
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Bake for 20 minutes or until a tester inserted near the center of the cake comes out clean. Cool in the pans for 10 minutes, then turn out onto wire racks to finish cooling.
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To make the filling, combine the flour with the sugar in a small saucepan.
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Add the egg, milk, and salt. Cook over low heat, stirring constantly, until the filling is smooth and thick.
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Stir in the vanilla. Chill in the refrigerator.
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Bake for 20 minutes or until a tester inserted near the center of the cake comes out clean. Cool in the pans for 10 minutes, then turn out onto wire racks to finish cooling.
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To make the filling, combine the flour with the sugar in a small saucepan.
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To assemble, spread the filling between the cooled cake layers and top with the frosting.