Preheat the oven to 350 degrees F. Grease and flour two 8-inch round cake pans.
Cream the shortening with the 1 cup sugar. Add 1 egg and beat until blended. Sift the 1-¾ cups flour together with the baking powder and ⅛ teaspoon salt. Add to the creamed mixture alternately with the milk. Stir in the vanilla. Divide the batter between the cake tins.
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.
To make the filling, combine the flour with the sugar in a small saucepan. Add the egg, milk, and salt. Cook over low heat, stirring constantly, until the filling is smooth and thick. Stir in the vanilla. Chill in the refrigerator.
To assemble, spread the filling between the cooled cake layers and top with the frosting.