Preheat the oven to 350 F. Line a 9x13-inch baking pan with foil, extending it up and over the sides, and spray the foil with nonstick cooking spray.
Combine the finely chopped chocolate and butter in a large bowl, and microwave it in 30-second increments, stirring after every 30 seconds to prevent overheating. When the chocolate is mostly melted, with just a few pieces remaining, stop heating it and stir until the chocolate is fully melted and smooth.
In a separate large bowl, whisk together the eggs and sugar. Add the melted chocolate mixture, and whisk that in as well. Finally, sift the flour, salt, baking powder, and cocoa powder over the bowl, and stir it in gently with a spatula. Spread the brownie batter in the prepared pan.
Bake the brownies at 350 F for about 20 minutes, until the top is shiny and crackly, and a toothpick inserted into the center comes out with a few moist crumbs attached. Let the brownies cool to room temperature before taking them out of the pan and cutting them.