How to Make It
Prepare the Cakes: Preheat oven to 350°F. Coat a 13- x 9-inch baking pan with cooking spray; dust with flour. Beat butter in a large bowl with an electric mixer fitted with a paddle attachment on medium-high speed until creamy, about 2 minutes; gradually add sugar, beating well. Stir together flour, baking powder, and salt in a bowl until combined; add to butter mixture alternately with milk, beginning and ending with flour mixture, beating well after each addition. Stir in vanilla and lemon extracts.
Beat egg whites with an electric mixer fitted with a whisk attachment on high speed in a separate bowl until stiff peaks form, about 2 minutes; fold into batter.
Pour batter into prepared baking pan. Bake in preheated oven until a wooden pick inserted in center comes out clean, about 35 minutes. Cool in pan 10 minutes. Remove from pan; let cool completely on a wire rack, about 1 hour.
Meanwhile, prepare the Frosting: Stir together egg whites, sugar, corn syrup, and cream of tartar in top of a large double boiler; add cold water, and beat with a hand mixer on low speed until just blended, about 1 minute. Place over boiling water; cook, beating constantly on high speed, until soft peaks form, about 8 minutes. Remove from heat; beat in vanilla.
Cut cooled cake into 2-inch rounds using biscuit cutter. Spread top and sides of small Cakes with Frosting. Sprinkle Cakes evenly with coconut.