Beat sugar and shortening at medium speed with an electric mixer until creamy. Add pumpkin, egg and vanilla in a small bowl; 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.
Drop by tablespoonfuls onto ungreased baking sheets. Bake at 350° for 15 to 20 minutes, to cool. Drizzle cookies with Brown Sugar Glaze.
Makes 2 dozen.
Brown sugar glaze:
Combine brown sugar, butter and milk in a small saucepan. Bring mixture to a boil over medium heat; boil 2 minutes. Remove from heat. Add powdered sugar. Beat at medium speed with an electric mixer until mixture is smooth.