In a large bowl, cream butter and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine flour and cocoa; add to creamed mixture just until combined. Stir in walnuts.
Spread into an ungreased 13-in. x 9-in. baking pan. Bake at 350° for 23-28 minutes or until a toothpick inserted near the center comes out clean. Cool on a wire rack.
For frosting, in a small bowl, beat butter until fluffy. Beat in the confectioners' sugar, cocoa, milk and vanilla until smooth. Spread over brownies. Cut into bars. Yield: 2 dozen.