1. Preheat oven to 375 degrees. Spray two 8-by-2-inch round cake pans with cooking spray and line with parchment paper rounds; set aside.

2. Sift together flour, baking powder, and salt into a medium bowl; set aside. In a 2-cup glass measuring cup, stir together milk and vanilla; set aside.

3. In the bowl of an electric mixer fitted with a paddle attachment, cream together the shortening and 1 cup sugar. With mixer on low speed, add flour mixture in three parts, alternating with milk mixture and beginning and ending with flour; beat until just combined.

4. In the clean bowl of an electric mixer fitted with the whisk attachment, beat egg whites on low speed until foamy. With mixer running, gradually add remaining 3 tablespoons sugar; beat on high speed until stiff, glossy peaks form. Do not overbeat. Gently fold a third of the egg-white mixture into the flour mixture until combined. Gently fold in remaining egg whites.

5. Divide batter evenly between prepared pans, smoothing with an offset spatula. Bake, rotating pans halfway through, until cakes are golden brown and a cake tester inserted into centers comes out clean, about 25 minutes.

6. Transfer pans to a wire rack to cool 15 minutes. Invert cakes onto wire rack; peel off parchment. Re-invert cakes and let them cool completely, top sides up.

7. Using a serrated knife, trim tops of cakes to make level. Place four strips of parchment paper around perimeter of a serving plate or lazy Susan. Place the first layer on the cake plate. Spread the top of the first layer with the filling. Top with the remaining layer, bottom side up. Spread entire cake with frosting; remove parchment paper strips.