Melt together chocolate chips and butter in the microwave, stirring after each 30-second increment.
Allow the chocolate mixture to cool for 5-10 minutes. While you are waiting, preheat the oven to 350 degrees F. Line a 9 by 13 pan with parchment or aluminum foil.
Pour your chocolate mixture into a mixing bowl and whisk in sugars.
Whisk in eggs one at a time.
Gently fold in flour, cocoa powder, and salt. Mix until thoroughly combined and no lumps remain.
Pour brownie batter into prepared 9" by 13" dish.
Bake for 30 minutes at 350 degrees F; the brownies are done when a knife inserted in the center comes out clean.
Once the brownies have cooled in the pan for 10 minutes, remove them brownies from pan using the parchment paper lining. Place them on a cookie sheet to cool completely, for 1-2 hours.
Using an electric mixer, beat together the butter and cream cheese until light and fluffy (2-3 minutes).
Add milk, food coloring, and peppermint extract, then slowly stir in the 2 cups of powdered sugar.
Apply frosting to brownies that are completely cool. Place frosted brownies in the refrigerator for at least 1 hour before adding the chocolate topping.
Melt butter and chocolate in a saucepan over medium heat, stirring constantly, until the chocolate chips are completely melted and the mixture is smooth. (Alternately, you could melt this in a microwave-safe bowl in 30 second increments. I prefer to use the stove for this section, as it helps the chocolate chips break down more completely.)
Pour this topping over the chilled, frosted brownies. Spread in an even layer and allow to cool completely (at least one hour, up to overnight) before slicing.
In order to preserve the picturesque brownies, slice them using a warm knife, cleaning it with a wet paper towel between each slice.