Cream together the shortening, peanut butter and sugars. Beat in egg. Combine the flour, baking soda, baking powder and salt; gradually stir into the peanut butter mixture. Cover and refrigerate dough for at least one hour.
Preheat oven to 375 degrees F (190 degrees C). Make small balls of dough. Flatten with fork dipped in flour to form cross-wise pattern.
Bake for 10-12 minutes in the preheated oven, or until just set. Remove from baking sheets to cool on wire racks.