Preheat the oven to 350°F. Line an 8x8 pan with parchment paper to form a sling. Lightly grease the pan.
Combine flour, cocoa, baking powder and salt in a large bowl and set aside.
In another bowl whisk together the sugar, egg whites, vegetable oil and vanilla extract until creamy.
Add egg mixture to dry ingredients, stirring just until blended.
Pour the brownie mixture into the prepared 8 inch square pan.
Bake at 350°F 20 to 23 minutes or until firm to the touch and a toothpick comes out with a few moist crumbs. Do not over-bake.
Cool completely. Cut into 9 squares.
Notes
If you are separating the eggs yourself, the easiest way to separate egg whites from egg yolks is to crack the egg into your hand over a small bowl. Hold the yolk in your hand while letting the white run through your fingers.
Lining the pan with parchment paper or aluminum foil will allow you to lift the entire baked brownies out of the pan for easier cutting once cooled. You can also grease the pan instead if you would prefer.
Make sure not to overbake these. You want the insides to be slightly gooey and the outsides firm.
It is essential that the brownies are completely cooled before slicing. Brownies will crumble if they are too warm when cut.