1. Preheat oven to 350°.
2. To prepare cake, line bottoms of 2 (9-inch) round cake pans with parchment paper. Coat pans lightly with cooking spray. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, 1/2 cup cocoa, baking powder, and 1/2 teaspoon salt in a bowl, stirring well with a whisk. Place 1 3/4 cups sugar and 1/2 cup butter in a large bowl; beat with a mixer at medium speed until light and fluffy (about 2 minutes). Add 3 eggs, 1 at a time, beating well after each addition. Add flour mixture and whole milk alternately to butter mixture, beginning and ending with flour mixture, and beat just until combined. Fold in vanilla.
3. Divide batter evenly between prepared pans. Bake at 350° for 27 minutes or until a wooden pick inserted in center comes out clean. Cool 25 minutes in pans on wire racks. Remove cakes from pans; cool completely on wire racks.
4. To prepare frosting, combine reduced-fat milk and 1/4 cup coconut in a small saucepan; bring to a boil. Remove from heat; let stand 15 minutes. Strain milk mixture through a sieve over a bowl; discard solids. Return milk to pan over medium heat. Combine 1/4 cup sugar, cornstarch, and 1 egg in a small bowl, stirring well with a whisk. Gradually add egg mixture to pan; bring to a boil, stirring constantly. Reduce heat, and cook 1 minute, stirring constantly with a whisk. Remove from heat; add 2 tablespoons butter, stirring until butter melts. Place pan in a large ice-filled bowl; let stand 15 minutes or until pastry cream cools to room temperature, stirring occasionally. Remove pan from ice. Spoon mixture into a bowl. Place plastic wrap on surface; chill.
5. Combine remaining 1/2 cup sugar and 2 tablespoons water in a saucepan; bring to a boil. Cook 3 minutes, without stirring, or until a candy thermometer registers 250°. Combine egg whites, cream of tartar, and dash of salt in a large bowl; beat with a mixer at high speed until foamy. Pour hot sugar syrup in a thin stream over egg whites; beat until stiff peaks form. Gently stir one-fourth of egg white mixture into chilled pastry cream; gently fold in remaining egg white mixture.
6. Place 1 cake layer on a plate; spread about 2 cups frosting over cake, leaving a (1/2-inch) border around outside edges. Top with remaining cake layer. Spread remaining frosting over top of cake. Sprinkle remaining 1/4 cup coconut evenly over top of cake.