Preheat your oven to 177 °C (175 °C). Line an 8x8 inch metal baking pan with parchment paper, leaving an overhang on two sides for easy removal. Lightly grease the parchment.

In a heatproof bowl set over a saucepan of simmering water (double boiler method), melt the unsalted butter and finely chopped bittersweet chocolate together. Stir occasionally until smooth and fully combined. Remove from heat and let it cool slightly.

In a large bowl, whisk together the granulated sugar, whole eggs, and egg yolk until the mixture is pale and slightly thickened, about 2-3 minutes. Stir in the vanilla extract.

Gently whisk the slightly cooled chocolate-butter mixture into the egg and sugar mixture until just combined. Be careful not to overmix.

In a separate small bowl, whisk together the all-purpose flour, unsweetened cocoa powder, and salt. Sift this dry mixture over the wet ingredients and fold gently with a spatula until just incorporated. Do not overwork the batter. If using, fold in the optional semisweet chocolate chips.

Pour the batter into the prepared baking pan and spread evenly. For an extra visual flair, sprinkle a few more chocolate chips on top.

Bake for 30-35 minutes, or until a toothpick inserted into the center comes out with moist crumbs attached, but not wet batter. The edges should be set.

Let the brownies cool completely in the pan on a wire rack. This chilling step is crucial for achieving the perfect fudgy texture and allows them to set properly for clean slicing.

Once fully cooled, use the parchment paper overhang to lift the brownies out of the pan. Slice into desired portions and serve.