Line a cookie sheet with parchment paper or foil; set aside. In a small bowl stir together powdered sugar, cocoa powder, cornstarch, and espresso powder; set aside.
In a medium mixing bowl beat egg whites and vanilla with an electric mixer on high speed until foamy. Gradually add the granulated sugar, 1 tablespoon at a time, beating until stiff peaks form (tips stand straight). Gradually fold in the cocoa mixture.
Transfer the mixture to a pastry bag fitted with a large star tip. Pipe twenty-four 2-inch stars onto the prepared cookie sheet. (Or drop mixture by rounded teaspoons onto the prepared cookie sheet.) Bake in a 250 degree oven for 1 hour. Cool on cookie sheet on wire rack. Remove from parchment paper.
In a small saucepan combine chocolate pieces and shortening. Cook and stir over low heat until chocolate is melted. Drizzle the melted chocolate over cookies. Makes 24 cookies.