Preheat oven to 350 degrees F.
In a mixer fitted with a whisk attachment, cream the butter. Add the brown sugar and continue mixing. Add the eggs, 1 at a time, and vanilla, then mix until well blended and fluffy.
In a separate bowl, sift together the dry ingredients. Add to the creamed mixture alternately with the applesauce. Fold in the raisins and walnuts. Pour batter into a greased and floured loaf or tube pan and bake until firm to the touch, about 40 to 45 minutes. Let cool in the pan, then turn it out, and dust with powdered sugar.