Space 2 racks evenly in the middle of an oven and preheat to 350°F. Line 2 baking sheets with parchment paper or with a silpat.
In a clean, dry, heatproof bowl, such as a glass Pyrex bowl, whisk together the egg whites and sugar. Set over but not touching simmering water in a small saucepan. Whisk constantly until the sugar is completely dissolved, about 5 minutes. Remove from the heat.
Pour the egg whites into a stand mixer (or use an electric mixer) fitted with the whisk attachment. Beat the egg mixture on high speed until stiff and glossy. Sift the cocoa powder over the meringue. Add the chocolate, then fold together gently with a rubber spatula until combined.
Drop the meringue by heaping tablespoons, spaced slightly apart, onto the prepared baking sheets. You can pipe them if you like. Bake for 9 minutes. Rotate the pans. (I turned the pans 180 degrees, and I also put the top pan on the bottom and vise versa.) Bake until the cookies are fluffy, full of cracks and spring back when touched, about 9 minutes more. Carefully pick up the parchment sheets and transfer the cookies, still on the parchment, to wire racks to cool. Makes about 28 meringues.