Combine the first 3 ingredients in a small bowl; stir well, and set the cocoa mixture aside.
Combine flour, sugar, baking powder, baking soda, and salt in a large bowl; make a well in center of mixture. Combine applesauce and next 5 ingredients (applesauce through egg) in a bowl; add to dry ingredients, stirring just until dry ingredients are moistened. Remove 1 cup of batter, and add to cocoa mixture; stir well. Spoon cocoa batter alternately with applesauce batter into a 9 x 5-inch loaf pan coated with cooking spray. Using the tip of a knife, swirl batters together. Bake at 350° for 1 hour or until a wooden pick inserted in center comes out clean. Let cool in pan 10 minutes on a wire rack; remove from pan, and let cool completely on wire rack. Sift the powdered sugar over loaf, if desired.