Not a full recipe but...
Pitted prunes, final volume will equal volume of eggs and/or fat
Put prunes in blender or food processor. Whip until very smooth. Substitute in place of eggs and/or fat in cake recipes in equal volume. Works especially well in chocolate cakes. It sounds gross but it really works. The best way is to use prunes plus egg whites only, but this won't help if you have to avoid the whole egg, so do a full substitution instead.
Another egg/fat substitute is applesauce. But I've never used it so I can't vouch for it.
(posted to rec.food.recipes 1/98)