Heat oven to 350°F. Spoon cookie dough into bottom only of greased or sprayed 9-inch square pan; press evenly in bottom of pan.
Bake 15 minutes. Meanwhile, in medium bowl, beat cream cheese and sugar with electric mixer on low speed about 30 seconds or until blended. Beat in vanilla and eggs, one at a time. Spread filling evenly over partially baked crust.
Bake 28 to 32 minutes longer or until puffed and center is just set. Cool 30 minutes on cooling rack. Refrigerate until cold, at least 1 hour. For bars, cut into 4 rows by 4 rows. Drizzle each serving with chocolate syrup. Store covered in refrigerator.