There are some lovely flourless chocolate cakes, but I've had trouble finding non-chocolate ones so I started experimenting and this came out well so I'm sharing. This is not very sweet--almost like a muffin--and it's low sugar and fat as well. I think I'll be eating it for breakfast!
1 cup rolled oats
1-2 Tbs cinnamon
1/2 cup sugar (optional--depending how sweet your applesauce is)
Put the oats in a food processor or blender or run through a grinder so they are a coarse flour. Add the applesauce, cinnamon and egg yolks so it makes a thick paste.
In a separate bowl, whip the egg whites until soft peaks form. Slowly add in the sugar to the whites.
Gently fold the apple-oat-cinnamon mix into the egg whites.
Put into a greased 7x11 or 9x9 baking dish. Bake at 300 for about 45 minutes (check with a toothpick to make sure it's done).
It's really good warm with butter :)