Heat oven to 350°F. Divide cookie dough into 12 equal pieces. With floured fingers, wrap 1 piece of dough around each peanut butter cup, shaping into ball. On ungreased cookie sheet, place 6 dough balls, arranging evenly apart. Refrigerate remaining 6 balls until ready to bake.
Bake 11 to 14 minutes or until golden brown. Cool 1 minute; remove from cookie sheet to cooling rack. Cool completely, about 15 minutes. Bake remaining balls of dough.
In small saucepan, melt chocolate chips and shortening over low heat, stirring constantly. Drizzle melted chocolate in crisscross pattern over cooled cookies. Let stand until glaze is set before storing.