Butter an 8 by 8 by 2-inch pan and line the bottom with a square of parchment or waxed paper.

Set a rack in the middle level of the oven and preheat to 350 degrees.

In a medium bowl, sift together cocoa, flour, baking powder and salt. In a separate bowl, beat together butter and sugar. Whisk in egg whites, apple sauce and vanilla. Stir flour mixture into apple sauce mixture until combined. Pour batter into prepared pan and bake for 35 to 40 minutes or until firm. Cool before cutting into squares.