Grease 8 inch square pan. In small bowl combine the flour, baking soda, and salt; set aside. in medium bowl mix together the egg, brown sugar and vanilla. Add the flour mixture and mix until well combined. Stir in the chopped walnuts.
Spread in the prepared pan. Bake at 350° for 18 to 20 minutes. Cut into squares while still warm from oven, but leave in pan to cool.