Preheat oven to 300 degrees F and line two baking sheets with parchment paper.
In the bowl of an electric stand mixer, beat egg whites and vanilla until soft peaks form. Gradually add sugar and beat until stiff peaks form. Sift cocoa over egg whites and gently fold until combined. Fill a pastry bag fitted with a large star tip (#1M or #8b). Pipe 1 1/4 inch stars on a baking sheet. O.k. to crowd but don't touch.
Bake 30 to 35 minutes. Cool on a rack.
In a microwave or double boiler, melt semi-sweet chocolate with shortening. Stir until smooth. Dip 1/2 of each cookie in the chocolate and place on parchment or wax paper to set.
Recipe adapted from 1999 Taste of Home Annual Recipes
This recipe was calculated using the exact brands and measurements I used to make this recipe. If you are following a strict diet please note changing anything will cause the nutritional info to change. My calculations are intended as a guide only.