1. Place 4 egg whites in a large bowl; let stand at room temperature 30 minutes. Line bottoms of 3 greased 9-in. round baking pans with parchment; grease parchment. Preheat oven to 350°.

2. Cream butter and 1 cup sugar until light and fluffy, 5-7 minutes; beat in extracts. In another bowl, whisk together flour, baking powder and salt; add to creamed mixture alternately with milk.

3. With clean beaters, beat the 4 egg whites on medium speed until soft peaks form. Gradually add remaining 1/2 cup sugar, 1 tablespoon at a time, beating on high after each addition until sugar is dissolved. Continue beating until stiff glossy peaks form. Fold into batter.

4. Transfer to prepared pans. Bake until a toothpick inserted in center comes out clean, 13-17 minutes. Cool in pans 10 minutes before removing to wire racks; remove paper. Cool completely.

5. For frosting, in a large heatproof bowl, whisk 5 egg whites, sugar, water and cream of tartar until blended. Place over simmering water in a large saucepan over medium heat; whisking constantly, heat mixture until a thermometer reads 160°, 2-3 minutes. Remove from heat; add vanilla. Beat on high speed until stiff glossy peaks form, about 7 minutes.

6. Spread between layers and over top and sides of cake. Cover with coconut. If desired, decorate with sprinkles. Store, uncovered, in refrigerator.