How to Make It
Combine orange juice and 1 tablespoon sugar in a small saucepan. Bring mixture to a boil over medium heat; cook 1 minute, stirring until sugar dissolves. Remove from heat; cool.
Preheat oven to 350°.
Weigh or lightly spoon flours and cornstarch into dry measuring cups; level with a knife. Combine flours, cornstarch, baking powder, xanthan gum, and salt in a medium bowl; stir with a whisk.
Place 1 cup sugar, oil, and butter in a large bowl; beat with a mixer at medium speed until blended. Beat in 2 teaspoons vanilla. Add flour mixture and milk alternately to sugar mixture, beginning and ending with flour mixture.
Beat 6 egg whites with a mixer at high speed until foamy; gradually add 1/4 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Fold egg whites into batter. Pour batter into 2 (9-inch) round cake pans coated with cooking spray.
Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool 10 minutes in pans on a wire rack; remove from pans. Cool completely on wire rack. Pierce entire surface of cake layers at 1/2-inch intervals with a wooden pick. Drizzle orange syrup over cakes. Let stand 20 minutes.
Combine 3 egg whites and next 4 ingredients (through 1/8 teaspoon salt) in the top of a double boiler. Cook over simmering water until a thermometer registers 160°, stirring constantly with a whisk. Pour egg white mixture into a large bowl; add 1 teaspoon vanilla. Beat at high speed until stiff peaks form and frosting is cool.
Place 1 cake layer on a plate; spread with 1/2 cup frosting. Top with second cake layer. Spread remaining frosting over top and sides of cake. Sprinkle coconut over top of cake. Chill 1 hour. Store cake loosely covered in refrigerator.