Into bowl of stand mixer, sift together cake flour, sugar, baking powder, and salt. Add shortening, 2/3 cup milk, and vanilla; beat 2 minutes. Add another 1/3 cup milk and egg whites. Beat 2 minutes more. Evenly distribute into cake pans. Bake approximately 25 - 30 minutes, until inserted cake tester comes out clean. Turn cake onto cooling rack. Cool completely before filling and frosting.