Prepare and bake brownies according to the package instructions. Let them cool completely.
In a medium bowl, beat butter until smooth. Add powdered sugar, milk, peppermint extract, and green food coloring if desired. Mix until creamy.
Spread the mint frosting evenly over cooled brownies. Refrigerate until set.
In a saucepan over low heat, melt chocolate chips with heavy cream, stirring until smooth.
Pour the chocolate ganache over the mint layer, spreading evenly.
Chill until the chocolate is set before slicing and serving.