Chop the dark chocolate into small pieces and set aside. Melt the chocolate and butter together in a microwave-safe bowl in 30-second bursts, stirring until smooth and glossy. Let it cool slightly while you prepare the next steps.
In a large mixing bowl, whisk together the sugar, eggs, and vanilla extract until the mixture is slightly frothy and well combined, about 1-2 minutes.
Pour the cooled chocolate and butter mixture into the egg mixture, gently folding with a spatula until fully incorporated and smooth.
Sift together the flour and cocoa powder, then gently fold them into the wet mixture just until no streaks remain. Be careful not to overmix to keep the brownies tender.
Pour the batter into a greased or parchment-lined 8-inch square baking pan, spreading it evenly with a spatula for a smooth top.
Bake in a preheated oven at 175°C (350°F) for about 20-25 minutes. The edges should be set and slightly cracked, while the center remains soft and slightly jiggly when shaken gently.
Insert a toothpick into the center—if it comes out with moist crumbs and no wet batter, the brownies are ready. Remove from the oven and allow to cool in the pan for at least 15 minutes.
Transfer the brownies to a wire rack to cool completely, then slice into squares. The center should be gooey and rich, with a shiny, cracked top. Serve warm or at room temperature for the best experience.
