Preheat oven to 350°F (175°C). Grease a 9-inch square baking pan or line with parchment paper.
In a medium bowl, combine flour, cocoa powder, baking powder, and salt.
In another bowl, mix applesauce, sugar, egg whites, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients and stir until combined.
Pour the batter into the prepared pan and smooth the top.
Bake for 20-25 minutes or until a toothpick inserted in the center comes out clean.
Let cool completely before cutting into squares.