Preheat oven to 350° F (180° C), and grease a 9x13 inch square baking dish.

Stir together the flour, corn starch, white sugar, brown sugar, cocoa powder, walnuts, baking powder and baking soda in a bowl, sifting with a fork to remove lumps. Pour in the eggs, apple sauce and margarine, and mix with a large spoon or electric mixer on low until the mixture forms a smooth batter, 3 to 5 minutes. Scrape the batter into the prepared baking dish.

Place a sheet of aluminium foil on the oven rack to prevent spills as the brownies rise, then fall during baking. Bake until a toothpick inserted in the centre of the brownies comes out clean, 40 to 45 minutes. For best results, cover the baking dish with foil for the first 20-25 minutes this technique helps the brownie to rise and keep from drying out too much.