Finely chopping the chocolate results in small shards that won't sink in the batter. Use a spring-loaded ice cream scoop to transfer batter to muffin cups with ease.
Preheat oven to 350 degrees. Line 24 standard muffin cups with paper liners. In a small bowl, combine espresso powder and 2 teaspoons hot water. Stir espresso and chocolate into batter; divide among muffin cups. Bake until a toothpick inserted in center of a cupcake comes out with a few moist crumbs attached, about 20 minutes, rotating halfway through. Let cool in pans on wire racks 5 minutes, then transfer cupcakes to racks and let cool completely. (Unfrosted cupcakes may be stored, in airtight containers, at room temperature, up to 2 days.)
Set a large bowl over (not in) a pot of barely simmering water. Add sugar, egg whites, and cream of tartar and whisk constantly until mixture is warm and frothy and sugar is dissolved, about 4 minutes. Remove bowl from heat and, using an electric mixer, beat on medium until soft peaks form, about 4 minutes. Increase speed to high and beat until whites form medium-stiff, glossy peaks, about 3 minutes.
Transfer frosting to a large zip-top bag and snip a 1/4-inch hole in one corner. Frost cupcakes, then finely grate some chocolate on top.
Chill Out Be sure cupcakes are completely cool before decorating, to avoid melting the frosting.
Icing on the (Cup)Cake You don't need fancy supplies to frost these treats -- a zip-top bag makes a fine stand-in for a pastry bag. Place it in a tall glass so it's easier to fill.