Preheat oven to 350 degrees F (175 degrees C). Grease a 9x9-inch baking pan.
Beat butter and 1/2 cup white sugar until light and fluffy. Beat in egg yolks.
Combine flour, baking powder and salt in bowl. Add flour mixture to butter mixture in two parts, alternating with milk and vanilla, beginning and ending with flour mixture. Spread in the prepared pan.
To Make Topping: Beat egg whites until soft peaks form; add 1/2 cup of the white sugar gradually, and beat until egg whites are stiff. Fold in the coconut. Put spoonfuls here and there over batter, smoothing as best you can.
Bake in preheated oven until meringue topping starts to brown and a toothpick inserted in the center comes out clean, 30 to 35 minutes.