Cream shortening in a medium mixing bowl; gradually add sugar, beating until light and fluffy. Add egg and vanilla, beating well.
Sift together flour, baking powder, and salt in a small mixing bowl; gradually add to creamed mixture, stirring well after each addition.
Press dough from a cookie press onto ungreased cookie sheets, using desired shaping disks. Bake at 350° for 12 to 15 minutes. Remove from cookie sheets, and cool completely on wire racks.
Spoon frosting into a pastry bag fitted with a star tip; decorate each cookie as desired.