Heat oven to 350°F. In ungreased 13x9-inch pan, break up cookie dough. With floured fingers, press dough evenly in bottom of pan to form crust. Bake 15 to 20 minutes or until light golden brown. Immediately sprinkle marshmallows evenly over crust.
Bake 1 to 2 minutes longer or until marshmallows just begin to puff. Cool while making topping.
In 4-quart saucepan, heat corn syrup, butter, vanilla and peanut butter chips over medium heat, stirring constantly, just until melted and smooth. Remove from heat. Stir in cereal and peanuts. Immediately spoon warm topping over marshmallows; spread to cover. Refrigerate until firm, about 45 minutes. For bars, cut into 6 rows by 6 rows.