Make One-Bowl Chocolate Cake Batter and bake following the sheet cake instructions.
Make the frosting: Whisk the sugar, egg whites, water, vanilla and coconut extracts, cream of tartar and salt in a large heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water). Keeping the bowl over the simmering water, beat with a hand mixer on medium-high speed until thick, glossy stiff peaks form, about 7 minutes. Remove the bowl from the pan and beat until slightly cooled, about 30 seconds.
Assemble the cake: Spread the frosting on the cake, making peaks with the back of a spoon. Toast the frosting with a kitchen torch until lightly browned. Top with toasted coconut flakes.