01 - Preheat your oven to 350°F. Line a 9x9-inch baking pan with parchment paper, allowing an overhang on two sides to easily lift the brownies later.
02 - In a heatproof bowl set over a saucepan of simmering water (creating a double boiler), melt the unsalted butter and semisweet chocolate designated for the brownie layer. Stir gently until the mixture is completely smooth. Remove from the heat and allow it to cool slightly.
03 - Whisk the granulated sugar into the cooled chocolate mixture. Then, incorporate the eggs one at a time, ensuring each is fully mixed before adding the next. Stir in the vanilla extract.
04 - Gently fold in the all-purpose flour and salt into the wet mixture. Mix just until combined; be careful not to overmix, as this can lead to tough brownies.
05 - Pour the brownie batter into the prepared pan and spread evenly. Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out with moist crumbs clinging to it. Allow the brownie layer to cool completely in the pan on a wire rack.
06 - For the mint frosting, beat the softened unsalted butter in a mixing bowl until it's light and creamy. Gradually add the powdered sugar and whole milk, continuing to beat until the frosting is smooth and fluffy. Mix in the pure peppermint extract and a few drops of green food coloring until you achieve your desired shade of green.
07 - Evenly spread the prepared mint frosting over the cooled brownie layer. Transfer the pan to the refrigerator and chill for at least 20 minutes to allow the frosting to set.
08 - To prepare the ganache, heat the heavy cream in a small saucepan over medium heat until it just begins to simmer. Pour the hot cream over the chopped semisweet chocolate and the tablespoon of unsalted butter in a heatproof bowl. Let the mixture sit undisturbed for 2 minutes, then stir until it's smooth and glossy.
09 - Carefully pour the chocolate ganache over the chilled mint layer, spreading it evenly across the surface. Return the pan to the refrigerator and chill for a minimum of 30 minutes, or until the ganache is fully set.
10 - Once thoroughly chilled and set, use the parchment paper overhangs to lift the entire brownie slab from the pan. Place it on a cutting board and cut into 16 equal squares. Serve chilled or at room temperature.