Preheat oven to 325°. Line 2 (12-cup) cupcake pans with paper liners.
For cupcakes, whisk together flour, baking powder, and salt in a medium bowl. Set aside.
In another bowl, beat egg yolks and 1 cup sugar with an electric mixer on high for 2 minutes. (It will be pale yellow and ribbonlike.) Add water and next 3 ingredients (through sweetened coconut); whisk to combine. Whisk in flour mixture. Transfer to a large bowl.
Place egg whites and cream of tartar in a large bowl. Beat with a hand mixer or stand mixer at medium speed until foamy, using clean, dry beaters. Gradually add the remaining 1/4 cup sugar. Increase speed to high, and continue beating about 2 minutes or until stiff peaks form. With a rubber spatula, fold in about 1/3 of the whipped whites into reserved batter. Gently fold in the remaining whites.
Fill the cupcake liners about 3/4 full with the batter. Bake for 20–25 minutes (rotating pans halfway through baking time) or until a toothpick inserted in the center of a cupcake comes out clean. Transfer the pans to a wire rack, and let cool for 20 minutes. Remove cupcakes from pan, and cool completely.
For frosting, combine first 4 ingredients (through vanilla extract) in the bowl of a stand mixer, and stir until combined. Set bowl over a saucepan filled with simmering water, and stir constantly until the sugar is dissolved and reaches 160° on an instant-read thermometer.
Transfer bowl to a stand mixer fitted with whisk attachment; beat on high 8–10 minutes or until stiff peaks form.
Fill a pastry bag fitted with a medium tip with the frosting. (You can also use a zip-top plastic bag, and make a small snip in one of the bottom corners.) Pipe out a dollop of frosting on each cupcake, and sprinkle with coconut. Serve and eat immediately.