Prepare the Pan: Preheat the oven to 350°F. Line an 8-inch square baking dish with parchment paper, leaving about a 2-inch overhang on two sides. Lightly coat the parchment and exposed pan with nonstick cooking spray, then set the prepared pan aside. Melt the Chocolate Mixture: Place the butter, semisweet chocolate, and Dutch-process cocoa powder in a heatproof bowl. Set the bowl over a pan of simmering water and melt the ingredients together, stirring until the mixture becomes smooth. Remove from the heat and allow it to cool slightly. Combine the Dry Ingredients: In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined. Set the mixture aside.
Beat the Eggs and Sugar: In a large bowl, use an electric mixer to beat the eggs, granulated sugar, and vanilla extract until the mixture becomes pale, about 4 minutes.
Add the Chocolate: Beat the slightly cooled chocolate mixture into the egg mixture until well incorporated and evenly combined.
Finish the Batter: Add the flour mixture to the chocolate mixture. Beat just until the ingredients are combined, scraping down the sides of the bowl as needed. Avoid mixing beyond this point.
Fill the Pan: Scrape the finished brownie batter into the prepared baking dish. Use a spatula to smooth the surface into an even layer.
Bake the Brownies: Bake at 350°F for 30 to 35 minutes. Check the center with a toothpick or thin knife; the brownies are ready when it comes out with a few crumbs attached. Do not over-bake.
Cool in the Pan: Let the baked brownies cool in the pan for 30 minutes.
Transfer to a Rack: Use the parchment overhang to lift the brownies from the baking dish, then transfer them to a wire rack. Allow them to cool completely before cutting.
Slice and Serve: Cut the cooled brownie slab into 16 small brownies or 8 larger brownies, depending on the desired serving size.
