Prep: Preheat the oven to 350°F. Line an 9x9" square baking pan with parchment paper on the bottom and up the sides of the pan. I like to overlap two sheets of parchment paper in a T-shape and secure the overhanging parchment to the pan with metal binder clips. Set aside.
Chocolate mixture: In a medium bowl, add the chopped chocolate and cocoa powder. Set aside.
Brown butter: In a small pan, heat the butter on medium heat until it has completely melted. Keep cooking it until the white milk solids separate out and the mixture bubbles and sizzles loudly. Stir often to help the milk solids cook evenly. Once the bubbling subsides, the mixture will begin to foam on the surface and the milk solids will begin to turn brown at the bottom of the pan. Remove the pan from the heat the moment the milk solids are golden brown and the mixture smells nutty.
Melt chocolate: Pour the browned butter over the chocolate and cocoa powder. Let it sit undisturbed for about 3 minutes. Stir the mixture until the chocolate has completely melted. Set aside.
Egg mixture: In a large mixing bowl, add the eggs, granulated sugar, and brown sugar. Use a whisk or electric hand mixer to mix until well-combined, about 3 minutes. While constantly whisking with one hand, slowly stream the brown butter-chocolate mixture into the egg mixture until combined.
Fold in flour: Add the flour and fold together with a spatula until combined. Don't overmix.
Fill pan: Transfer the brownie batter to your lined pan. Use an offset spatula to spread the batter into the corners of the pan and into an even layer.
Bake: Bake brownies for about 28-30 minutes or until a toothpick inserted in the middle comes out mostly clean but with some wetness.
Cool: Let the brownies cool in the pan on a wire rack at room temperature or in the fridge while you prepare the mascarpone cream. The brownie layer can still be warm when adding the tiramisu topping but the sides of the pan should be cool to prevent the mascarpone from melting.