Beat sugar and shortening at medium speed with an electric mixer until creamy. Add pumpkin, egg, and vanilla, beating until blended; set aside.
Combine flour, baking soda, salt, and cinnamon in a small bowl; gradually add to shortening mixture, beating well. Fold in chocolate chips.
Drob by tablespoonfuls onto ungreased baking sheets. Bake at 350° for 15 to 20 minutes or until golden and browned on bottom. Remove to wire racks to cool. Drizzle cookies with Frosting.