This is our familys favorite cake -- we found the recipe on a box of raisins, I think, in the 1950s. It used to call for 1/2 cup of oil, but by increasing the applesauce it no longer needs it.
Mix dry ingredients together, then add the applesauce and stir. Bake at 325 degrees for 45-60 minutes, depending on the size of pan you use. (More for smaller, deeper pans, less for 9 x 13 pans.) Its done when a toothpick can be inserted and pulled out clean.
The cake is so rich I don't put frosting on it; my mother used to sprinkle powdered vegan sugar on top to give it a nice look.