01 - Preheat the oven to 350°F. Grease a 9x9 inch square baking pan and line it with parchment paper, leaving enough overhang on the sides to lift the brownies out later.
02 - Place the chopped dark chocolate and butter in a heatproof bowl set over a pot of barely simmering water. Stir occasionally until completely melted and smooth. Alternatively, melt in the microwave in 30-second bursts, stirring between each interval. Let the mixture cool slightly.
03 - In a large mixing bowl, whisk together the granulated sugar, brown sugar, eggs, and vanilla extract vigorously until the mixture turns pale and becomes slightly thickened, about 2 minutes.
04 - Pour the slightly cooled melted chocolate mixture into the egg and sugar mixture. Stir with a whisk or spatula until evenly combined and glossy.
05 - Sift the flour, cocoa powder, baking powder, and salt directly into the wet mixture. Using a spatula, gently fold the dry ingredients into the batter until just combined. Be careful not to overmix, as this can make the brownies tough.
06 - If using, gently fold in the chopped nuts and/or chocolate chips until evenly distributed throughout the batter.
07 - Pour the batter into the prepared baking pan and use a spatula to spread it evenly, smoothing the top.
08 - Bake for 22 to 25 minutes, or until the edges are set and pull away slightly from the pan while the center remains slightly soft and fudgy. A toothpick inserted into the center should come out with moist crumbs attached, not clean.
09 - Remove from the oven and allow the brownies to cool completely in the pan on a wire rack before lifting them out using the parchment overhang and slicing into 12 squares.