Lightly coat an 8x8x2-inch baking pan with nonstick cooking spray.
In a large bowl combine flour, granulated sugar, 1/4 cup cocoa powder, the baking powder, and salt. Stir in milk, applesauce, and vanilla until thoroughly mixed. Pour into prepared pan.
In a small bowl combine the hot water, brown sugar, 1/4 cup cocoa powder, and the coffee granules. Carefully pour water mixture over cake batter. Bake in a 350 degree F oven for 45 minutes. Spoon warm cake and pudding into dessert dishes. Serve with cappuccino chunk ice cream. Makes 10 servings.