Preheat oven to 350 degrees Fahrenheit. In the bowl of an electric mixer, combine brownie mix, vanilla, flour, butter and egg. Scoop or form into 1 1/2" balls and place 2" apart on a greased or non stick baking mat lined cookie sheet.
Bake for approximately 8-9 minutes. If you want the cookies to have flatter tops, press down the dough balls slightly before baking. If it looks like the first sheet of cookies in the oven is spreading out too much, add 1-2 Tbsp. more flour to the remainder of the dough.
Allow cookies to sit on sheets for a few minutes before removing them to a cooling rack to cool completely.
Make mint frosting by adding powdered sugar, milk, mint extract and green food coloring to a mixing bowl. Melt butter in a separate bowl in microwave and add to mixing bowl. Mix until combined. Dip cooled cookies halfway in the mint icing and place them in the refrigerator until the icing is completely set.