Arrange a rack in the middle of the oven and heat the oven to 325°F. Line an 8-inch or 9-inch square baking pan with parchment paper, then spray with cooking spray. (I used a 9-inch pan, so if you want thicker brownies, go for the 8-inch pan and add some extra time to your baking.)
Place oil into a microwave-safe medium bowl and heat in 4 to 6 (5-second) bursts until warm but not hot. Add unsweetened cocoa powder and whisk until completely smooth and combined. Let sit for 4 or 5 minutes so the cocoa can bloom. Meanwhile, prepare the dry and wet ingredients.
In a medium-sized bowl, place dry ingredients of all-purpose flour, salt, and baking powder in a small bowl and whisk to combine, set aside.
For the wet ingredients, in a large bowl or stand mixer, place eggs, powdered sugar and brown sugar together and using a mixer, beat on medium-high speed until fluffy and lighter in color, 2 1/2 to 3 minutes. Beat in 1 teaspoon vanilla extract until just combined.
Add 1/2 of the cocoa mixture to the egg mixture and beat on medium-high speed until shiny and fully combined, about 4-5 minutes.
Add the flour mixture and beat on low speed until fully combined. Add the remaining cocoa mixture and continue to beat on medium-high speed until shiny and fully combined, 1 to 2 minutes. Transfer to the baking pan and spread into an even layer.