Preheat Oven: Preheat your oven to 180°C (356°F) and position the rack in the middle or slightly higher.
Prepare Baking Tray: Prepare an 8-inch (20x20 cm) baking tray by greasing it and lining with baking paper, allowing the paper to overhang for easy removal of the brownies.
Brown the Butter: In a pan over low heat, melt the butter, stirring every 15 seconds, until it starts to foam, bubble, and then turns to a light brown color with a nutty aroma. Turn off the heat.
Mix Cocoa and Vanilla with Butter: Add the cocoa powder and vanilla to the browned butter, stirring well to combine. Set aside.
Beat Sugar and Eggs: In a large bowl, mix the sugar and eggs until light and fluffy. This step is crucial for achieving the characteristic shiny top layer on the brownies.
Combine Wet and Dry Ingredients: Gently fold the brown butter mixture into the egg and sugar mixture. Then, gradually add the flour and salt, folding until just combined without overmixing.
Add Optional Chocolate: If using, fold in the chopped dark chocolate.
Bake: Pour the batter into the prepared tray, spreading evenly. Bake for approximately 35 minutes, or until done.
Cool and Serve: Allow the brownies to cool completely in the tray before cutting into pieces. Serve as is, or with a scoop of vanilla ice cream for an extra treat.