Preheat your oven to 350°F (175°C). Line your 9x9 inch baking pan with parchment paper, allowing some overhang on the sides for easy removal later.
In a double boiler or a microwave-safe bowl, melt 1 cup of unsalted butter and 3 ounces of chopped semisweet chocolate together, stirring until smooth and glossy. Be careful not to overheat, as burnt chocolate can ruin the flavor.
Once melted, remove from heat and whisk in 1 cup of granulated white sugar and 1/2 cup of unsweetened cocoa powder until fully combined.
Add 1/2 cup of mascarpone cheese to the chocolate mixture, followed by the 3 large eggs and 2 teaspoons of vanilla extract. Whisk until everything is integrated and creamy.
Sift in 1/2 cup of all-purpose flour and 1/4 teaspoon of salt. Gently fold the dry ingredients into the wet mixture until just combined. Be careful not to overmix, as this can lead to denser brownies.
Pour the 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 cooling, prepare the chocolate ganache. In a small saucepan, combine 6 ounces of chopped semisweet chocolate, 6 tablespoons of whipping cream, and 3 tablespoons of unsalted butter. Heat over low heat, stirring until smooth and glossy.
Once the brownies are completely cooled, drizzle the ganache over the top. Allow it to set for a few minutes before slicing into squares. Enjoy your delicious Chocolate Mascarpone Brownies with a scoop of ice cream or a dollop of whipped cream for an extra treat!