For the brownie batter: In a medium saucepan, add 1/2 cup butter and unsweetened chocolate. Melt over low heat. Remove from heat once melted and combined. Let cool for 10 minutes.
Next, preheat an oven to 350 degrees. Line a 9X9 baking dish with parchment paper. Spray with non-stick cooking spray for extra insurance.
In a small bowl combine 2/3 cup all-purpose flour and 1/4 tsp baking soda.
Next, stir in 1 cup of granulated sugar into the reserved cooled chocolate mixture. Add 2 eggs, one at a time, and beat until combined. Stir in 1 tsp vanilla extract and reserved flour mixture until combined. Pour the brownie into the prepared baking dish.
For the cookie dough: In mixer fitted with a paddle attachment beat 1/4 cup butter with shortening until combined. Next, add in the remaining 1 cup sugar, cream of tartar, 1/4 tsp baking soda, and a pinch of salt. Beat in the last egg, 1/4 tsp vanilla extract, and the peppermint extract. Lastly, beat in the remaining 1 cup of all-purpose flour. Once everything is combined, fold in the chopped Andes mints.
Using an ice cream scoop, drop mounds of cookie dough over the brownie batter. Bake for about 30 minutes or until browned and set. Let cool on a wire rack before slicing. Cut into bars and enjoy!