3/4 cup large egg whites (about 6), at room temperature
2 teaspoons almond extract
1 teaspoon vanilla extract
2 1/4 cups cake flour
1 3/4 cups granulated sugar
4 teaspoons baking powder
1 teaspoon table salt
12 tablespoons unsalted butter , softened
1. For the cake: Set oven rack in middle position. (If oven is too small to cook both layers on a single rack, set racks in upper-middle and lower-middle positions.) Heat oven to 350 degrees. Coat bottom and sides of two 9-inch-by-1 1/2-inch or 2-inch round cake pans with 1 tablespoon shortening each. Sprinkle 1 heaping tablespoon of all-purpose flour into each pan; roll pans in all directions to coat. Invert pans and rap sharply to remove excess flour.
2. Pour milk, egg whites, and extracts into 2-cup glass measure, and mix with fork until blended.
3. Mix cake flour, sugar, baking powder, and salt in bowl of electric mixer at slow speed. Add butter; continue beating at slow speed until mixture resembles moist crumbs, with no powdery ingredients remaining.
4. Add all but 1/2 cup of milk mixture to crumbs and beat at medium speed (or high speed if using handheld mixer) for 1 1/2 minutes. Add remaining 1/2 cup of milk mixture and beat 30 seconds more. Stop mixer and scrape sides of bowl. Return mixer to medium (or high) speed and beat 20 seconds longer.
5. Divide batter evenly between two prepared cake pans; using rubber spatula, spread batter to pan walls and smooth tops. Arrange pans at least 3 inches from the oven walls and 3 inches apart. (If oven is small, place pans on separate racks in staggered fashion to allow for air circulation.) Bake until cake needle or toothpick inserted in the center comes out clean, 23 to 25 minutes.
6. Let cakes rest in pans for 3 minutes. Loosen from sides of pans with a knife, if necessary, and invert onto greased cake racks. Reinvert onto additional greased racks. Let cool completely, about 1 1/2 hours.