Applesauce cake is a mystery to me. Of course, a lot of my baking involves apple sauce! For instance, I used it in a devil's food cake recipe recently. So it's not so strange. It's really wonderful actually for keeping baked goods moist.
The great part is that the
applesauce in the applesauce cake works as a binder, so there's no eggs to replace in the
random internet recipes you pull up. For instance: This recipe
is easily veganized by using vegan margarine - though personally I'm
not a big fan of baked goods with raisins in them. Same with this one.
So have at it! Show me your applesauce cake magic. And have fun!