Preheat oven to 350 degrees F (175 degrees C). Grease and flour one 8x8 inch pan.
Combine butter and milk in large saucepan. Place over low heat until shortening melts. Remove from heat, add the brown sugar and egg. Stir until well blended. Stir flour into sugar mixture. Stir in vanilla and nuts. Spread evenly into prepared pan.
Bake at 350 degrees F (175 degrees C) for 20 to 25 minutes or until toothpick inserted in middle comes out clean or the sides start to pull away from the pan. Cool and cut into 2x2 inch squares.