Preheat your oven to 175°C (350°F) and line the square pan with parchment paper, leaving overhang on the sides for easy removal.
In a microwave-safe bowl, melt the butter until smooth and fragrant, then pour it into a mixing bowl.
Add the sugar to the melted butter and whisk until the mixture is shiny and just combined, about 1-2 minutes. The aroma of chocolate and caramel should fill the air.
Crack in the eggs one at a time, whisking vigorously after each addition until the mixture is smooth, glossy, and slightly thickened.
Stir in the vanilla extract, blending it into the batter until evenly incorporated.
Sift together the cocoa powder, baking powder, and a pinch of salt into a separate bowl. Then, gradually fold these dry ingredients into the wet mixture, using a spatula or spoon, just until the batter is uniform and no streaks remain. Be careful not to overmix to keep the brownies fudgy.
Pour the thick, glossy batter into the prepared pan and spread it evenly with a spatula, tapping the pan gently on the counter to release air bubbles.
Bake in the preheated oven for 20 to 25 minutes, until the edges are slightly pulled away from the pan and the top has a shiny, crackly surface. Insert a toothpick into the center; a few moist crumbs should cling when done.
Remove the pan from the oven and let the brownies cool in the pan for about 10 minutes, then lift them out using the parchment overhang and transfer to a wire rack to cool completely. This helps set the fudgy interior while preventing sogginess.
Once cooled, cut the brownies into squares with a sharp knife. Sprinkle with sea salt flakes on top for a sweet-salty finish, if desired.
Serve the brownies plain, dusted with powdered sugar, or with a scoop of vanilla ice cream for extra indulgence. Enjoy the rich, fudgy texture and crackly top with each delicious bite.
