Preheat oven to 350 degrees. Grease a 9-inch by 13-inch pan.
In a large bowl, mix butter, sugar, and 1/2 teaspoon vanilla. Add eggs and milk; mix well. Stir in flour and cocoa; then stir in walnuts.
Spread in prepared pan. Bake 40 minutes, until brownies begin to pull away from the sides of the pan.
Just before brownies are done, melt chocolate chips with condensed milk and 1-1/2 teaspoons vanilla in a heavy saucepan. Immediately spread over hot brownies; cool, chill, and cut into bars.
Recipe submitted by Joyce on 7/10/00