Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a large bowl, mix melted butter and 2 cups of sugar until well combined. Add 4 eggs, one at a time, beating well after each addition.
Stir in 1 cup of flour, 1 cup of cocoa powder, ½ teaspoon of salt, 1 teaspoon of vanilla extract, and ½ teaspoon of peppermint extract until just combined. Fold in 1 cup of mini chocolate chips.
Pour the brownie batter into the prepared baking pan and spread evenly.
In another bowl, beat 16 oz of softened cream cheese and ½ cup of sugar until smooth. Add 1 egg and ½ teaspoon of peppermint extract, and beat until well combined. If using, add a few drops of green food coloring and mix until the color is even.
Spread the cheesecake mixture over the brownie batter in the pan.
Bake in the preheated oven for 35 minutes, or until the cheesecake layer is set and a toothpick inserted into the center comes out with a few moist crumbs.
Allow to cool completely in the pan before cutting into squares and serving.