Press cookie dough into a greased 13-in. x 9-in. x 2-in. baking pan. Bake at 350 degrees for 10 minutes (The original recipe says 10 minutes, but I would only bake for 5-7 minutes, especially if you use my cookie recipe).
Meanwhile, in a saucepan, combine the marshmallows, chocolate chips and butter. Cook and stir over low heat until melted and smooth. Transfer to a large bowl; cool. Beat in eggs and vanilla. Combine the flour, baking powder and salt; stir into marshmallow mixture. Stir in nuts. Spread over cookie crust. Bake for 30-35 minutes or until a toothpick inserted near the center comes out clean. Cool on a wire rack.
For frosting, in a small saucepan, combine the marshmallows, milk, butter and chocolate. Cook and stir over low heat until smooth. Remove from the heat; beat in confectioners’ sugar until smooth. Frost brownies. Cut into bars.