Preheat oven to 350℉. Grease an 8 x 8 inch square pan.
Melt butter in a small saucepan, pour into a mixing bowl, and stir in sugar.
Melt sugar over low heat in the small saucepan, add to butter-sugar mixture, and blend well.
Add eggs and nuts, stirring until well blended.
Gradually add flour, blending thoroughly. Stir in vanilla.
Pour into a prepared pan, and bake for 30 minutes, or until knife inserted in center comes out clean. Remove pan and cool on wire rack before cutting into squares.