1. Place a rack in middle of oven; preheat to 350°. Coat 2 (9- x 1 1/2-inch) round cake pans with cooking spray. Dust with flour; shake out excess, and set aside.
2. To make cake: Place 1 cup sugar and 1/3 cup coconut in a food processor; process until coconut is finely ground. Transfer to a large deep bowl. Add butter and remaining 1/3 cup sugar to bowl; beat with an electric mixer at medium-high speed until light and fluffy (about 5 minutes). Add eggs, one at a time, beating well after each addition. Combine flour, baking powder, and salt in medium bowl. Reduce mixer speed to low. Add flour mixture alternately with coconut milk, beginning and ending with flour mixture. Beat in vanilla. Evenly divide batter between the 2 prepared pans.
3. Bake cakes until a wooden toothpick inserted in centers comes out clean (about 35 minutes). Leave oven on. Cool cakes in pans on wire rack for 10 minutes. Invert cakes onto wire rack; cool completely.
4. To make frosting: Place coconut on a large baking sheet; toast until golden brown (about 10 minutes), stirring twice. Place egg whites, sugar, cream of tartar, and salt in a large deep heatproof bowl set over about 1 1/2 inches of simmering water; beat with an electric mixer at medium-high speed until peaks form when beaters are lifted (about 7 minutes). Remove bowl from saucepan; continue beating until frosting is cooled (about 3 minutes). Beat in vanilla.
5. Carefully place 1 cake layer on a plate. Using a spatula, spread a layer of frosting over top of cake; top with remaining cake. Spread remaining frosting over top and sides of entire cake. Sprinkle toasted coconut over entire cake.