Combine the sugar, butter, cream cheese, egg and vanilla in a large bowl. Beat at medium speed of electric mixer, scraping bowl often, until light and fluffy. Add flour; beat until well mixed. Divide dough in half; wrap each half in waxed paper. Refrigerate 2 hours or until firm.
Preheat oven to 375℉. Roll out dough to ⅛" thickness on lightly floured surface. Cut out with lightly floured cookie cutter. Place 1" apart on ungreased cookie sheets. Bake 7-10 minutes or until edges are very lightly browned. Remove immediately to wire racks to cool completely.
Melt chocolate chips and shortening in small saucepan over low heat 4-6 minutes or until melted. Dip half of each cookie into melted chocolate. Refrigerate on cookie sheets or trays lined with waxed paper until chocolate is firm. Store, covered, in refrigerator.