Step 1Heat the oven to 175 degrees. In the bowl of a stand mixer or in a large mixing bowl with a hand mixer, whip the egg whites until frothy. With the mixer running, slowly add the sugar until incorporated and the meringue forms soft peaks, then rain in the powdered sugar and continue to whip just until the meringue forms stiff peaks when the mixer is removed.
Step 2Using a pastry bag outfitted with a large round tip (about one-half inch in diameter), pipe 12 small half circles onto a parchment-lined baking sheet. They should be one-half to three-fourth-inches tall and 1 1/2 inches wide, and should be spaced about 3 inches apart. Using the back of a spoon or small offset spatula, smear the unfinished part of each circle so that each meringue has a teardrop shape. Sprinkle one-eighth teaspoon coconut evenly over each of the meringues.
Step 3Bake the meringues for 2 to 3 hours, until completely dry. Set aside in a dry place, or leave in the oven with the heat turned off. Baked meringues will keep for up to one day at room temperature in a cool, dry place.