Preheat oven to 350℉. Grease a 9x13 baking pan and line with parchment paper for easy lifting, set aside.
Melt chocolate and ½ cup of butter in a double boiler, stirring regularly until smooth. Remove from the heat and allow it to cool slightly.
In a medium bowl, beat the sugar, 3 eggs, vanilla, and flour until just combined. Add the chocolate mixture and beat until combined.
Spread the brownie batter in the prepared baking pan and bake for 15 minutes, or until set, but not cooked all the way through.
In a stand mixer, beat cream cheese, 2 Tbsp butter, and cornstarch until fluffy. Gradually beat in sweetened condensed milk, then beat in remaining egg, peppermint extract and green food coloring.
Pour over brownie layer. Bake for 30- 35 minutes or until set. Once baked, cool to room temperature before making the ganache.
While you make the ganache, place the brownies in the fridge so that they will be slightly chilled. Heat the cream in the microwave until hot, in 20 second bursts. Pour over the chocolate and let sit for 5 minutes. Mix until smooth.
Pour the ganache over the bars, allow it to cool, then chill in the fridge until set before cutting into bars and serving.