Melt butter and chocolate in a saucepan over low heat.
Beat eggs and sugar at medium speed with an electric mixer until well blended. Gradually add chocolate mixture to egg mixture, beating at low speed until blended. Gradually add vanilla and flour, beating until blended. Stir in walnuts. Pour into a lightly greased, aluminum foil-lined 8-inch square pan.
Bake at 325° for 35 minutes. Cool completely on a wire rack. Cut into squares.
Adapted from The Beach House Cookbook by Barbara Scott-Goodman (Chronicle Books, 2005)