Preheat your oven to 350°F. Line an 8x8-inch metal baking pan with parchment paper, leaving a 2-inch overhang at all sides.
Place chocolate and butter in a heatproof bowl set over a saucepan of barely simmering water and stir until melted and smooth. You can also melt the chocolate in the microwave on 50% and stirring every 20 seconds.
Combine eggs with sugar in a large bowl and beat for 2 minutes using an electric hand mixer until pale, thick and fluffy. Mix in vanilla and salt. Add warm chocolate mixture and whisk it in until evenly incorporated. The mixture should tighten up and become thick and glossy.
Sift cornstarch, cocoa powder and baking powder into a separate small bowl and whisk to blend evenly. Add it to chocolate mixture. Stir it in until evenly blended.
Spread batter evenly into prepared pan and smooth out the top. Bake for 20-22 minutes until a toothpick inserted into the center comes out with a few moist crumbs attached and the top is shiny crinkly and puffed. It will sink as it cools. Transfer pan to a wire rack and let cool completely in the pan before slicing. For even fudgier brownies, let them set overnight in the fridge before slicing.