Preheat your oven to 350Β°F (180Β°C). Prepare an 8x8 inch baking pan by lining it with parchment paper, leaving a little overhang to easily lift out your brownies later. You can also just lightly grease the pan.
Chop the butter into pieces and finely chop the dark chocolate. Place them together in a microwave-safe bowl.
Melt the butter and chocolate gently: heat on medium power in the microwave for 45-second bursts, stirring well after each, until smooth. (Alternatively, melt over a double boiler.) Let this rich chocolate mixture cool down to just warm, not hot.
Into the cooled chocolate mixture, whisk in the granulated sugar, eggs, and vanilla extract until everything is nicely combined and glossy.
Next, gently stir in the all-purpose flour, cocoa powder, and salt. Mix until you no longer see any dry flour or lumps β don't overmix!
Pour the brownie batter into your prepared pan and spread it evenly. Bake in the center of your preheated oven for 26-32 minutes, or until a toothpick inserted into the middle comes out with a few moist crumbs, but no wet batter.
Let the brownies cool completely in the pan for several hours. This step is key for perfect fudgy texture and clean frosting!