Adjust an oven rack to the lower middle position. Preheat the oven to 350°F. Grease a 9 by 13-inch baking pan and line a parchment sling.
In a medium saucepan over medium-low heat, melt the butter and the bittersweet chocolate until both are melted and smooth. Remove from the heat and add the cocoa powder, stirring until smooth. Set aside to cool slightly.
In a small bowl, whisk the flour, baking powder, and salt.
In a large bowl, whisk the eggs, oil, sugars, and vanilla. Add the slightly cooled chocolate mixture and whisk until smooth. Add the flour mixture and stir with a spatula until just combined. Pour the batter into the prepared pan and bake 22 to 27 minutes, until the sides of the brownies have set, the top is beginning to crackle and look glossy, and a wooden skewer or toothpick inserted into the center comes out with crumbs. The batter on the skewer should not be wet, but should have a good amount of crumbs clinging to it.
Transfer the pan to a wire rack and let cool completely. Use the parchment paper sling to gently lift the brownies from the pan. Cut them into squares.