Adjust an oven rack to the lower-middle position and heat the oven to 350 degrees F. Line an 8-inch square baking pan with two pieces of foil that extend beyond the edges of the pan (to serve as handles to lift the cooled brownies out of the pan). Spray the foil with vegetable oil spray.
Melt the chocolates and butter in a medium heatproof bowl set over a saucepan of barely simmering water (or in the top of a double boiler), stirring occasionally, until smooth. Whisk in the cocoa powder until smooth. Set aside to cool slightly.
Whisk the eggs, sugar, vanilla, and salt together in a medium bowl until combined, about 15 seconds.
Whisk the warm chocolate mixture into the egg mixture. Using a wooden spoon, stir in the flour until just combined.
Transfer the batter to the prepared pan. Using a spatula, spread the batter into the corners and smooth the surface. Bake until slightly puffed and a toothpick or wooden skewer inserted into the center of the brownies comes out with a few moist crumbs attached, 35 to 40 minutes.
Cool the brownies on a wire rack to room temperature, about 2 hours.
Loosen the edges with a paring knife and lift the brownies from the pan using the foil extensions. Cut the brownies. The cut brownies can be wrapped in plastic wrap and refrigerated for up to 5 days.