In a large mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar and baking soda; beat until combined, scraping sides of bowl occasionally. Beat in egg, orange juice concentrate, and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Bake in a 375 degree F oven about 8 minutes or until edges are lightly browned. Cool on cookie sheet for 1 minute. Transfer to wire racks: cool completely. Spread cookies with Orange Frosting. If desired, sprinkle with finely shredded orange peel. Makes about 36 cookies.
In a medium mixing bowl stir together orange juice concentrate, orange peel, and powdered sugar until smooth.