In an extra--arge bowl, allow egg whites to stand at room temperature for 30 minutes. Line four large cookie sheets with parchment paper or lightly grease and flour the sheets; set aside.
Beat egg whites, vanilla, coconut extract, cream of tartar, salt and cinnamon with electric mixer on high speed until soft peaks form (tips curl). Gradually add powdered sugar, 2 tablespoons at a time, beating until stiff peaks form (tips stand straight). Fold in coconut, half at a time.
Using an ice cream scoop with 1-inch bowl (or a tablespoon measure), drop coconut mixture in mounds 2 inches apart on prepared cookie sheets. Bake in a 325 degrees F oven for 10 to 12 minutes or until bottoms are light brown. Cool on wire racks.
In a small saucepan, combine chocolate and shortening. Cook and stir over low heat until chocolate melts. Cool slightly. Dip bottoms of cookies in melted chocolate mixture or drizzle chocolate over tops. Place on a piece of waxed paper and let stand until set. Makes about 80 cookies.
Layer cookies between waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze undipped cookies for up to 3 months. Thaw cookies; dip bottoms of cookies in melted chocolate.