Preheat oven to 350°F. 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 2 teaspoons of the vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Stir in chocolate chips. Set aside.
Prepare brownie mix as directed on package, adding remaining 1 teaspoon vanilla and peppermint extract. Spread in greased 13x9-inch baking pan.
Bake 15 minutes. Drop cookie dough by tablespoonfuls on brownie, covering the top evenly. (Batter will spread during baking)
Bake 20 to 25 minutes longer or until cookie top is golden brown. Cool in pan on wire rack. Cut into bars.