Preheat oven to 350 degrees F (175 degrees C). Melt the butter in a 7x11 inch baking dish, and tilt the pan to coat all of the sides; set aside.
In a medium bowl, stir together the brown sugar, flour, and baking soda. Mix in the eggs and vanilla until smooth, then stir in the walnuts. Pour over the melted butter.
Bake in the preheated oven for 20 minutes, or until the edges begin to brown. Cool, then cut into squares, and dust with confectioners sugar.
