Preheat the oven to 175 C. Line an 8" square pan non-stick baking paper, leaving a little overhang. You could use a smaller pan as well for thicker brownies, increasing the baking time as needed.
In a bowl placed over a pot of simmering water, melt the butter, chocolate and cocoa until you have a smooth mixture (see notes). Let this cool while you get the rest of the batter ready.
Beat the eggs, sugar and vanilla in a large bowl till pale and thickened, about 3 to 4 minutes. This is where you're ensuring a crust forms, so beat away! An electric mixer on medium to high speed will get the best results.
Add the cooled chocolate mixture to the egg mixture and beat again till combined.
Sift in the flour, baking powder and salt. Stir slowly until no flour is visible. The batter is quite thick. At this stage, optionally, stir in chocolate chips, chopped nuts or other mix-ins.
Spread the batter evenly into the prepared dish, smoothen the top and bake for 15 to 20 minutes, till a toothpick poked in the center comes out with moist crumbs but no wet batter. Don't bake them till the toothpick comes out fully clean, that means the brownies will dry out as they cool down. Under-baking just slightly ensures they keep cooking as they cool, but remain soft and gooey.
Allow the brownies to cool completely at room temperature before slicing. Best stored at room temperature in an airtight tin for 2 days in humid environments, after which they can be kept in the fridge for a week, or even frozen for a month. Happy baking!