Preheat your oven to 180°C (350°F). Line the baking pan with parchment paper, leaving extra overhang for easy removal.
Melt the butter gently in a saucepan over low heat until smooth and fragrant, then remove from heat.
Stir the cocoa powder and vanilla extract into the melted butter until well combined; the mixture will smell rich and chocolatey.
In a large bowl, whisk the eggs until slightly frothy, then add the brown sugar and whisk until the mixture is smooth and slightly thickened.
Pour the slightly cooled chocolate mixture into the egg and sugar, whisking steadily to create a shiny, smooth batter that smells intensely chocolatey.
Gently fold in the flour using a spatula until just combined, being careful not to overmix, to keep the batter tender.
Stir in the chopped bittersweet chocolate or chocolate chips, distributing evenly throughout the batter.
Pour the batter into the prepared pan and spread it evenly with a spatula, smoothing the top for a uniform surface.
Bake in the preheated oven for 20–25 minutes, until the top is crackly and shiny, but the center still jiggles slightly when gently shaken.
Remove the pan from the oven and let it cool on a wire rack for at least 15 minutes. The edges will firm up while the center remains fudgy and moist.
Use the parchment overhang to lift the bars out of the pan. Slice into squares while slightly warm or fully cooled, and enjoy!