Line 13x9-inch pan with foil, with ends of foil extending over sides; spray with cooking spray. Prepare brownie batter as directed on package; pour into prepared pan.
Bake 25 min. or until top is shiny and center is almost set. (Do not overbake.)
Beat cream cheese, sugar and vanilla in medium bowl with mixer until blended. Add eggs, 1 at a time, mixing on low speed after each just until blended. Pour over brownie layer in pan. Evenly scatter cookie dough pieces over batter.
Bake 30 min. or until center of cheesecake layer is almost set. Cool completely. Refrigerate dessert 4 hours.
Use foil handles to remove dessert from pan just before serving. Melt chocolate chips as directed on package; drizzle over dessert. Refrigerate 15 min. or until chocolate is firm.