Preheat your oven to 175°C (350°F) and line an 8-inch square baking pan with parchment paper, leaving overhang for easy removal.
In a heatproof bowl, melt the butter and chopped dark chocolate together over simmering water or in short bursts in the microwave, stirring until smooth and glossy. Let it cool slightly so it doesn’t cook the eggs.
In a large mixing bowl, whisk together the granulated sugar, eggs, and vanilla extract until the mixture becomes slightly frothy and well combined.
Pour the slightly cooled chocolate-butter mixture into the egg mixture, whisking continuously to create a shiny, unified batter.
Sift the cocoa powder into the bowl and gently fold it in with a spatula until the mixture is smooth and evenly colored, taking care not to overmix.
Sprinkle the flour over the batter and fold gently until just combined. The batter should be thick and glossy.
Pour the batter into the prepared pan and spread evenly with a spatula. Tap the pan lightly on the counter to remove air bubbles.
Bake in the oven for 20-25 minutes, until the edges are set but the center still jiggles slightly when gently shaken. The top should crack and look shiny.
Remove the brownies from the oven and let them cool in the pan for 15 minutes. Then, lift out using the parchment overhang and transfer to a wire rack to cool completely.
Once cooled, slice into squares with a sharp knife, wiping between cuts for clean edges. Serve at room temperature for the best fudgy texture.
Enjoy the dense, chewy, and intensely chocolatey brownies, perfect for satisfying any chocolate craving!