Preheat oven to 350°F and position a rack in the center of the oven. Line a 9-inch square baking pan with aluminum foil (see notes above).
In a large bowl, whisk together the cocoa, flour, baking powder, and salt.
In another large bowl, beat the eggs very well until foamy and thick — about 1 minute of vigorous whisking.
Melt the butter in a medium saucepan over medium heat — it should be hot and bubbling lightly. Add the sugar and whisk until well very combined — I like to use my flat-bottomed whisk here. The mixture should be nearly emulsified and should look like wet sand.
Pour the melted butter-sugar mix into the eggs and whisk constantly until very well combined. Be sure to scrape the bottom of the pot to extract any lingering sugar/butter. Add the vanilla to the egg-sugar mix, and whisk to incorporate.
Add the dry ingredients to the wet, and whisk until smooth.
Spread the batter into the prepared pan and bake for approximately 37-40 minutes. Insert a toothpick straight into the center. If it comes out clean or with just a few moist crumbs, the brownies are done.
Let cool completely in pan on rack (at least 30 minutes) before cutting. Brownies can be made two to three days in advance.
