Beat eggs and vanilla together in mixing bowl. Add in brown sugar, flour, baking soda, salt and walnuts. Mix until well blended.
Melt the butter in a 9-inch square pan. Pour the batter into the pan and bake for 20 to 25 minutes, until firm to the touch.
While bars are still hot, loosen with a spatula and turn out onto wax paper, buttered side up. Dust with confectioners' sugar while warm and cut into squares.
