In a large bowl, combine the first six ingredients. Spread into a greased 13-in. x 9-in. baking pan. Bake at 350° for 30-35 minutes or until a toothpick inserted in the center comes out clean (do not overbake).
Meanwhile, in a small bowl, cream butter and sugar until light and fluffy. Beat in the egg, coffee and vanilla until well blended. Stir in walnuts and chocolate chips. Spread over brownies. Bake at 350° for 17 minutes or until set. Cool on a wire rack.
For icing, in a small saucepan melt the chocolate chips and butter over low heat until chips are melted, stirring constantly. Whisk in coffee and enough milk to reach a drizzling consistency. Drizzle over warm brownies. Cool before cutting.