Preheat your oven to 350°F (175°C). Prepare your baking pan by greasing it lightly or lining it with parchment paper, leaving some overhang for easy removal later.
In a microwave-safe bowl, combine the unsalted butter and 3 ounces of chopped semisweet chocolate. Microwave in 30-second intervals, stirring in between until melted and smooth. Allow the mixture to cool slightly.
Once the chocolate mixture has cooled, stir in the granulated white sugar and unsweetened cocoa powder until well combined.
Next, add the mascarpone cheese to the chocolate mixture. Whisk until smooth. Then, add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Sift together the all-purpose flour and salt, then fold them into the chocolate mixture using a rubber spatula. Be careful not to overmix; you want the batter to be just combined.
Pour the brownie batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for 25-30 minutes or until a toothpick inserted into the center comes out with a few moist crumbs.
While the brownies are baking, make the ganache. In a medium heatproof bowl, combine the 6 ounces of chopped semisweet chocolate, 6 tablespoons of whipping cream, and 3 tablespoons of unsalted butter. Microwave in 30-second intervals, stirring until everything is melted and smooth.
Once the brownies are done, remove them from the oven and allow them to cool in the pan for about 10 minutes. Gently lift the brownies out using the parchment paper. Pour the chocolate ganache over the top, spreading it evenly. Let the ganache set before slicing.