Melt the butter and chopped chocolate in a medium saucepan over medium heat. Stir the mixture constantly for about 5 minutes. Remove pan from heat and pour mixture into large mixing bowl for further cooling for about 10 minutes (it just needs to slightly cool, not fully).
Place you oven rack in the lower third position and preheat oven to 350 degrees. Line the bottom and sides of a 9x13 inch baking pan with parchment paper with an overhang on all sides. This will help you to easily lift the brownies out of the pan when cool. Set baking dish aside.
Whisk the granulated sugar and brown sugars into the cooled chocolate/butter mixture. Add the eggs, one at a time, whisking until smooth after each addition. Whisk in the vanilla. Gently fold in the salt, flour, and cocoa powder. Set mixture aside.
Pour batter into prepared 9x13 pan and cook for 35 minutes. You will know the brownies are done, when they start to pull away from the sides of the pan. When you test with a toothpick in the center of the brownies, there should only be a few moist crumbs.
Let the brownies cool completely in the pan on a wire rack. This should take about 1 hour. After they have completely cooled, lift the parchment paper overhang and placed cooled brownies with parchment paper still under it on a baking sheet.
In a stand mixer, beat the butter on medium speed until smooth and creamy. This should take about 2 minutes.
Add the powdered sugar and milk. Beat for 2 minutes on low speed. Increase to high speed and beat for 1 additional minute.
Add the peppermint extract and food coloring drops and beat on high for 1 minute.
Frost the cooled brownies and place the brownies still on the baking sheet in the fridge to set for 2 hours. Its important the let the frosting set so its an easier process to spread the the chocolate layer on the mint frosting.
Melt the butter and chocolate chips in a medium saucepan on medium heat. Stir constantly for about 5 minutes. Once the chocolate is melted and smooth, pour evenly over the mint frosting layer.
Spread the melted butter and chocolate mixture gently with a small spatula.
Place the brownies, still on the baking sheet in the fridge to chill for 2 hours. The chocolate will be set, but a little soft. If you chill the brownies in the fridge overnight, the chocolate will harden. After the 2 hours, if you decide to chill more, cover with plastic wrap lightly, to avoid drying out.
Adapted from Sally's Baking Addiction