Preheat oven to 175°C (350°F). Grease and line the base of an 8-inch (20-cm) brownie pan or square cake pan with overhanging baking paper.
Place butter in a microwave-safe bowl and cover with a small plate. Microwave at medium or 50% power for 30 second intervals until fully melted and hot. Alternatively, you can melt butter in a saucepan over low heat on a stove top.
While the butter is still hot, tip in the brown and white sugars and stir vigorously to melt. If using a saucepan, add the sugars to the melted butter and heat until hot, but not bubbling. The mixture should look shiny as you stir. Set aside to cool.
Meanwhile, break the eggs into a separate bowl. Whisk or beat until foamy.
Gently fold into the butter-sugar mixture (remember, it's got to be cool enough) until well incorporated
Stir in the vanilla extract until well combined.
Add the flour, baking powder, salt and cocoa powder. Give it a good stir until the batter is smooth and there aren't remaining specks of flour. Mix just enough, do not over-stir! If adding nuts or chocolate chips, gently fold into the batter here.
Pour the batter into the prepared brownie or cake pan. Bake at 175°C (350°F) for 30 to 35 minutes. Do not overcook. Check by inserting a toothpick into the centre. If it comes out with moist sticky crumbs, it's perfect. If the toothpick comes out coated with wet, shiny dough clinging to it, continue to bake for longer.
Once the brownies are out of the oven, immediately run a knife around the edges to prevent the brownies from sinking in the centre. Let it cool completely in the pan. Remove from the pan by lifting the overhang.