Heat oven to 350°F. In large bowl, beat butter, powdered sugar and vanilla with spoon. Stir in flour. (If dough is crumbly, mix in 1 to 2 tablespoons butter or margarine, softened.)
Roll dough 1/2 inch thick on lightly floured surface. Cut into small shapes by hand or use cookie cutters. Place 1/2 inch apart on ungreased cookie sheet.
Bake 14 to 16 minutes or until set and bottoms are light golden brown. Immediately remove from cookie sheet to wire rack. Cool completely, about 30 minutes.
In small microwavable bowl, microwave chocolate chips and shortening uncovered on High 1 to 1 1/2 minutes or until melted; stir until smooth. Dip half of each cooled cookie into melted chocolate. Place on waxed paper until chocolate is set