In a medium bowl, combine coconut, sugar, flour, orange peel and salt. Add egg whites and vanilla. Stir until combined. Add 1/4 cup of the chocolate pieces. Stir until combined.
Drop 1 rounded teaspoon of mixture onto the prepared cookie sheets 2 inches apart. Bake for 18 minutes or until light brown.
Transfer to a wire rack, and allow to cool completely.
In a small saucepan, melt remaining 1/2 cup chocolate pieces and shortening over low heat. Stir until chocolate melts.
Drizzle chocolate mixture over cookies.
Notes
Cookies can be refrigerated in between wax paper layers in an airtight container for up to 3 days.