Preheat oven to 350 degrees F with a rack in the middle.
Grease a 8-inch (or 9-inch) square dark metal pan with softened butter, then line with parchment paper, leaving overhang on all sides. Grease the parchment paper with more softened butter. Reserve.
Place the butter and half of the chocolate (4 ounces) in a large microwave-safe bowl and microwave, uncovered, for 30 seconds. The butter should have melted by now, but the chocolate will still be solid. Give it a good stir and microwave again, this time for 15 seconds. Repeat until the chocolate has melted. Alternatively, you can melt the butter and chocolate on a double boiler on the stove.
Wait for the melted chocolate to cool slightly and then add the cocoa powder, sugar and brown sugar. Stir until smooth.
Add the eggs and egg yolk, one at a time, stirring until combined.
Stir in the vanilla extract. Mix really well until you reach the "ribbon stage", meaning when you lift your spoon, the batter falls back into the bowl in ribbons.
Place a fine mesh sieve over the bowl and sift the salt and flour into the brownie batter. Mix just until combined.
Fold in the remaining chopped chocolate, mixing to spread it evenly into the batter.
Pour the batter into the prepared pan, smoothing the top with a spatula.
Bake until lightly puffed on top, 20-25 minutes, depending on how fudgy you like your brownies. (see notes)
Remove the pan from the oven and let them cool completely.
Use the parchment paper to lift the cooled brownies out of the pan and cut into 9 to 16 squares before serving.