Grind toasted almonds in food processor. Lower oven temperature to 325 degrees F. Line cookie sheet with parchment paper or lightly spray with non-stick cooking spray.
Stir together ground almonds, coconut and orange peel; set aside. Stir together sugar and cocoa; set aside. Beat egg whites in large bowl on medium-high speed of mixer until soft peaks form. Gradually add sugar mixture, about 2 tablespoons at a time, beating on high speed of mixer until stiff peaks form and sugar is dissolved.
Gently fold almond mixture into egg-white mixture. Drop by slightly rounded teaspoons onto prepared cookie sheet.
Bake 18 to 20 minutes or until firm. Remove from cookie sheet to wire rack. Cool completely.
Combine chocolate chips and shortening in medium microwave-safe bowl. Microwave at HIGH (100%) 1 minute; stir. If necessary, microwave at HIGH an additional 15 seconds at a time, stirring after each heating, just until chips are melted when stirred. Dip half of each cookie in chocolate mixture. Place on wire racks over wax paper until chocolate is set. Store cookies, loosely covered in containers, at room temperature.