Adjust an oven rack to the lower-middle position and preheat the oven to 350°F (177°C). Spray an 8-inch square baking pan with nonstick cooking spray.

Cut or tear two 16-inch sheets of foil or parchment. Fold each sheet lengthwise once to make each about 8 inches wide. Fit one sheet into the greased pan so it covers the bottom and two opposite sides (leave an overhang). Fit the second sheet perpendicular to the first so the pan is fully lined and you have two overhanging handles. Spray the liner with nonstick cooking spray.

Set a medium heatproof bowl over a saucepan of barely simmering water (the water should not touch the bottom of the bowl). Add the 5 ounces chopped semisweet or bittersweet chocolate, the 2 ounces chopped unsweetened chocolate, and the 8 tablespoons butter to the bowl. Stir occasionally until the chocolate and butter are fully melted and the mixture is smooth.

Whisk the 3 tablespoons cocoa powder into the melted chocolate mixture until smooth. Remove the bowl from the pan and let the chocolate mixture cool until warm to the touch (so it will not cook the eggs when combined), about 3–5 minutes.

In a separate medium bowl, whisk together the 3 large eggs, 1¼ cups (250 g) granulated sugar, 2 teaspoons vanilla extract, and ½ teaspoon salt until combined, about 15 seconds.

With the egg mixture whisking, slowly pour the warm chocolate mixture into the eggs in a thin, steady stream to temper the eggs. Continue whisking until fully combined and smooth.

Add the 1 cup (125 g) all-purpose flour to the chocolate-egg mixture and stir with a wooden spoon until just combined. Do not overmix.

Pour the batter into the prepared pan and use a rubber spatula to spread it evenly into the corners and level the surface.

Bake on the lower-middle rack until the top is slightly puffed and a toothpick inserted in the center comes out with a few sticky crumbs clinging to it, 35 to 40 minutes.

Cool the pan on a wire rack to room temperature, about 2 hours. Use the foil or parchment overhang to lift the brownies from the pan and transfer them to a cutting board. Cut into squares and serve.