Pre-heat oven to 350 degrees F (175 degrees C). Lightly grease a 9 x 9 x 1-3/4 inch pan.
Sift together flour, baking powder and salt and set aside. In large bowl, beat together butter, sugar, egg and vanilla until smooth.
Stir in the flour mixture and the nuts until well blended. Spread evenly in prepared pan. Bake 25-30 minutes or until surface springs back when gently pressed. Cool slightly. While still warm, cut into bars with a sharp knife.