Preheat the oven to 350°F. Lightly grease an 8" x 8" pan., In a medium bowl, combine butter, cocoa, oil, sugar, eggs, applesauce, and vanilla. Mix well., In a separate bowl, mix flour, baking powder, baking soda, and salt., Add dry ingredients to wet ingredients, stirring just to combine. Spread the batter in the pan., Mix sugar, chopped nuts, and chocolate chips together. Sprinkle over batter., Bake brownies for 30 to 35 minutes. Allow to cool slightly before cutting., Store, loosely covered, for 3 days at room temperature. Freeze for up to 3 months.