(2 sticks) unsalted butter, at room temperature, plus more for the pan
all-purpose flour, spooned and leveled, plus more for the pan
large egg whites, at room temperature
whole milk, at room temperature
pure vanilla extract
14-ounce package sweetened shredded coconut (about 5 cups)
- Heat oven to 350° F. Butter an 11-by-17-inch rimmed baking sheet and line with parchment; butter the parchment and dust lightly with flour. Whisk together the flour, baking powder, baking soda, and salt in a medium bowl. In a separate bowl, whisk together the egg whites, milk, and vanilla.
- Beat the butter and sugar in a large bowl with an electric mixer on medium-high until light and fluffy, 2 to 3 minutes.
- Reduce mixer speed to low; add the flour mixture and milk mixture in alternate additions, beginning and ending with the flour mixture. Mix until just combined.
- Transfer the batter to the prepared sheet. Bake until the cake springs back lightly when pressed, 15 to 20 minutes. Cool, then transfer to a cutting board.
- Using a long, serrated knife, cut the cake into 4 pieces of equal size, slicing crosswise and lengthwise through the center.
- Place one layer of the cake on a serving platter and frost the top with ⅔ cup of the frosting. Repeat with 2 of the remaining layers. Top with the final layer. Frost the top and sides of the cake with the remaining 2 cups of frosting. Press the coconut into the top and sides of the cake.