Make the Brownie Batter. Preheat the oven to 350°F and grease and line a 9x9-inch metal baking pan with parchment paper. Whisk the melted butter with both sugars, then whisk in the eggs and vanilla until smooth and slightly thickened. Stir in the flour, cocoa powder, and salt just until combined, then fold in the chocolate chips.
Bake and Cool. Spread the batter evenly in the prepared pan and bake for 25–27 minutes, or until the edges are set and just beginning to pull away from the pan and a toothpick inserted in the center comes out with several moist crumbs but no wet batter. Cool completely in the pan for about 1 hour before frosting.
Make the Mint Frosting. Beat the softened butter until creamy, then gradually mix in the powdered sugar. Add the heavy cream, peppermint extract, and vanilla and beat for 2–3 minutes, until light and fluffy. Add 2–3 drops of green food coloring and mix until evenly colored.
Frost and Chill. Spread the mint frosting evenly over the completely cooled brownies. Refrigerate for 30 minutes, or until the frosting is firm to the touch. If your kitchen is particularly warm, chill for 30–40 minutes.
Make and Add the Ganache. Place the chocolate chips in a heat-safe bowl. Heat the heavy cream in the microwave in 15–20 second intervals until hot and just beginning to bubble. Pour it over the chocolate chips and let stand for 2 minutes, then stir until smooth and glossy. Let the ganache cool for 10 minutes so it remains pourable without melting the mint frosting, then spread it evenly over the chilled mint layer.
Chill and Slice. Refrigerate for 60–70 minutes, or until the ganache is completely set. Lift the brownies from the pan using the parchment and cut into 9 large squares or 16 smaller squares. For the cleanest layers, use a hot, sharp knife, wiping it clean between each cut.