Spray round micro-proof baking dish, 7-1/4 X 2-1/4 inches or 8 X 1-1/2 inches with a vegetable cooking spray. Line bottom with a round of plastic wrap. Re-spray lightly.
In small micro-proof bowl combine cocoa and 1/3 cup water; microwave on high( full power) 40-50 seconds until very hot and slightly thickened.
In medium bowl combine flour, sugar, baking soda, baking powder and salt. Wisk or stir dry ingredients together until thoroughly mixed.
In another small bowl combine the applesauce, the remaining 1/3 cup hot water, egg whites, and the vanilla.
Add the chocolate mixture to the applesauce mixture and blend. Add the applesauce/chocolate mixture to the dry ingredients and stir together with a fork or wisk. Blend ingredients gently and as little as possible to achieve mostly smooth batter. If you overbeat, you will get a rubbery texture in the cake.
Pour batter into the prepared pan. Microwave on high 5-6 minutes without turning until cake begins to pull away from sides (some moist spots may remain but will disappear on standing). Let stand 5 minutes; invert onto serving plate. Peel off plastic wrap; cool. Frost. Serve. Makes 1-8 inch layer.