Step 1: Preheat your oven to 350°F (175°C). Line an 8×8 inch (or 9×9 inch for thinner brownies) baking pan with parchment paper, leaving an overhang on two sides for easy removal. Lightly grease the parchment paper.
Step 2: In a large, microwave-safe bowl, combine the unsalted butter and chopped chocolate. Heat in 30-second intervals, stirring well after each, until completely melted and smooth. Set aside to cool slightly.
Step 3: In a separate large bowl, whisk together the granulated sugar and room temperature eggs vigorously for 2-3 minutes, until the mixture is light in color and slightly thickened. Stir in the vanilla extract.
Step 4: Pour the slightly cooled chocolate and butter mixture into the egg and sugar mixture. Whisk until just combined, being careful not to overmix.
Step 5: In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking powder, and salt. Sift the dry ingredients into the wet mixture.
Step 6: Gently fold the dry ingredients into the wet ingredients using a spatula until just a few streaks of flour remain. Do not overmix the batter.
Step 7: Pour the batter into your prepared baking pan and spread evenly with a spatula.
Step 8: Bake for 25-30 minutes for an 8×8 inch pan, or 20-25 minutes for a 9×9 inch pan. The brownies are done when a toothpick inserted into the center comes out with moist crumbs, not wet batter. Avoid overbaking for fudgy results.
Step 9: Remove the pan from the oven and let the brownies cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Once cooled, cut into squares and serve.