In a bowl, with an electric mixer on medium speed, beat butter and sugar until smooth. Beat in egg, orange peel, and vanilla until well blended, scraping down sides of bowl as needed.
In another bowl, stir together flour, cornstarch, baking powder, and salt. Stir or beat into butter mixture until well blended. Stir in coconut. Cover bowl and chill until dough is firm, about 2 hours.
Shape dough into 1-inch balls. Arrange about 2 inches apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets. With a lightly floured fork, flatten each ball to about 1/4 inch thick.
Bake cookies in a 375° oven until lightly browned, 8 to 10 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. With a wide spatula, transfer cookies to racks to cool completely.
Note: Nutritional analysis is per cookie.