Preheat your oven to 350°F (175°C). This ensures perfectly baked brownies.
In a double boiler or microwave, melt the 1 cup of unsalted butter and the 3 ounces of chopped semisweet chocolate together. Stir until smooth and set aside to cool slightly.
In a large mixing bowl, whisk together the granulated sugar and unsweetened cocoa powder until well combined.
To the sugar and cocoa mixture, add the mascarpone cheese, and mix until smooth. Then, add the 3 large eggs and 2 teaspoons of vanilla extract. Whisk until fully incorporated.
Pour the melted chocolate and butter mixture into the bowl with the other ingredients. Stir until combined.
Sift in the 1/2 cup of all-purpose flour and 1/4 teaspoon of salt. Gently fold the mixture until just combined, being careful not to overmix.
Pour the brownie batter into a greased 8x8 inch baking pan, spreading it evenly. Bake in the preheated oven for 20-25 minutes, or until the edges look set and a toothpick inserted in the center comes out with a few moist crumbs.
While the brownies are baking, prepare the ganache. In a small saucepan, combine the 6 ounces of chopped semisweet chocolate, 6 tablespoons of whipping cream, and 3 tablespoons of unsalted butter. Stir over low heat until melted and smooth.
Once the brownies are finished baking, remove them from the oven and let them cool for about 10 minutes. Pour the ganache over the top and spread it evenly.
Allow the brownies to cool completely in the pan. Once cooled, slice into squares and enjoy!