Preheat oven to 325°F. Prepare brownie mix as directed on package, adding 1 teaspoon of the vanilla and peppermint extract. Unroll pie crusts. Line 2 (9-inch) pie plates with pie crusts. Spoon 1/2 of the brownie batter into each pie plate. Bake 25 minutes.
Meanwhile, mix flour, baking soda and salt in medium bowl. Set aside. Beat butter and sugars in large bowl with electric mixer on medium speed until light and fluffy. Add egg and remaining 2 teaspoons vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Stir in chocolate chips.
Drop 1/2 of the cookie dough by tablespoonfuls on brownie in each pie. Spread cookie dough to cover the top evenly. Cover edge of crust with strips of foil to prevent excessive browning.
Bake 35 to 40 minutes or until cookie top is golden brown. Cool completely on wire rack. Serve with Vanilla Whipped Cream, if desired.