Preheat oven to 350 degrees. Grease cookies sheets.
Mix together flour, baking powder, baking soda and salt. Stir 1/2 cup orange juice and 1 teaspoon orange zest into the flour mixture.
Cream shortening and sugar together. Mix egg into the sugar mixture thoroughly. Slowly blend flour mixture into the egg and sugar mixture. Drop by teaspoonful onto greased cookie sheet.
Bake for 8 - 10 minutes.
Make the icing: Mix confectioners' sugar and 2 tablespoons butter together until smooth. Pour 2 tablespoons orange juice and 1 teaspoon orange zest into the sugar and butter mixture, mix well. When the cookies have cooled, spread the icing generously over the tops of the cookies.
Tip: I often use fresh squeezed orange juice and fresh orange zest. When using fresh orange zest, I usually double the amount to 2 teaspoons.