Mix together in a bowl with a mixer the shortening, butter, sugar, eggs, and flavoring.
In another bowl whisk together the flour, baking powder, and salt.
Stir the flour mixture into the butter mixture.
Chill dough at least 1 hour.
Once chilled roll the dough out to 1/8 inch thick on a floured board.
Cut with cookie cutters and place on an un-greased cookie sheet.
Sprinkle with sprinkles if desired.
Bake at 400 degrees for 6 to 8 minutes. Just bake until the cookies are set and slightly brown on the bottom side.
Cool on a wire rack.
Notes
If you don't want to use cookie cutters, you can roll the dough into balls and drop them on the cookie sheet and flatten them with the bottom of a glass.