Preheat your oven to 175°C (350°F). Line your baking pan with parchment paper, leaving a slight overhang for easy removal. Gather all your ingredients and tools.
Place the chopped dark chocolate and butter into a small saucepan. Melt them together over low heat, stirring constantly until the mixture is smooth and glossy. Remove from heat and let cool slightly.
In a large bowl, whisk the sugar and eggs until the mixture becomes slightly frothy and well combined, about 2 minutes.
Pour the slightly cooled chocolate mixture into the egg mixture. Gently fold with a spatula until fully combined and shiny.
Sift the cocoa powder directly into the bowl and fold it in carefully. Then, add the flour and vanilla extract, folding just until no streaks remain. Be gentle to keep the brownies tender.
Pour the batter into the prepared pan, spreading it evenly with a spatula. Give the pan a gentle tap on the counter to settle the batter and release any air bubbles.
Bake for 20 to 25 minutes, until the edges are just golden and the top has a shiny, crackly surface. Check doneness by inserting a toothpick—moist crumbs should cling but not wet batter.
Remove the pan from the oven and allow the brownies to cool in the pan for at least 15 minutes. For cleaner slices, refrigerate for an additional 30 minutes.
Use the parchment overhang to lift the brownies out of the pan. Slice into squares with a sharp knife, wiping it clean between cuts for neat edges.
Serve the brownies slightly warm or at room temperature, perhaps with a dusting of powdered sugar or a dollop of whipped cream. Enjoy the rich, fudgy texture with a complex chocolate flavor.
