To prepare cake, coat 3 (8-inch) round cake pans with cooking spray; line bottoms of pans with wax paper. Lightly coat wax paper with cooking spray; dust pans with 1 tablespoon flour.
Lightly spoon 2 1/2 cups flour into dry measuring cups, and level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Place 2 cups sugar and 6 tablespoons butter in a large bowl; beat with a mixer at medium speed for 2 minutes or until well blended. Add egg substitute and eggs to sugar mixture; beat well. Add flour mixture and coconut milk alternately to sugar mixture, beginning and ending with flour mixture. Stir in 1/4 teaspoon extract.
Spoon batter into prepared pans. Sharply tap the pans once on countertop to remove air bubbles. Bake at 350° for 25 minutes or until a wooden pick inserted in the center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Remove wax paper; discard. Cool cakes on wire racks.
To prepare frosting, combine 1 cup sugar and 1/4 cup water in a saucepan; bring to a boil. Cook 3 minutes, without stirring, or until a candy thermometer registers 250°. Combine egg whites, cream of tartar, and 1/8 teaspoon salt in a large bowl; using clean, dry beaters, beat with a mixer at high speed until foamy. Pour hot sugar syrup in a thin stream over egg whites, beating at high speed until stiff peaks form, about 3 minutes. Reduce mixer speed to low; continue beating until egg white mixture cools (about 12 minutes).
Beat 1/4 cup butter until light and fluffy; stir in 1/4 teaspoon extract, if desired. Fold in 1 cup egg white mixture. Fold butter mixture into remaining egg white mixture, stirring until smooth.
Place 1 cake layer on a plate; spread with 1 cup frosting. Repeat twice with cake layers and 1 cup frosting, ending with cake layer; spread remaining frosting over top and sides of cake. Sprinkle with toasted coconut. Chill until set.