Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
Mix together flour, baking powder, baking soda and salt. Stir 1/2 cup orange juice and 1 teaspoon rind into the flour mixture.
Cream shortening and white 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 to 10 minutes.
Make the icing: Mix confectioner’s sugar and 2 tablespoons butter together until smooth. Pour 2 tablespoons orange juice and 1 teaspoon orange rind into the sugar and butter mixture, mix well. When the cookies have cooled spread the icing generously over the tops of the cookies.