In the bowl of a standing mixer with the paddle attachment, add 1 cup of unsalted butter, 1/2 cup of vegetable oil, 1 cup of granulated sugar, and 1 cup of powdered sugar. Mix until combined, then turn the mixer on high and whip for 1-2 minutes.
Fold in 2 eggs, 1/4 cup sour cream, and 1 tsp peppermint extract.
In a separate bowl combine 5 1/2 cups all-purpose flour, 1/2 tsp baking soda, 1/2 tsp cream of tartar and 1/2 tsp fine sea salt.
Turn the mixer on low and slowly pour the dry ingredients into the wet ingredients just until a dough forms.
Fold in the 1 cup of chopped peppermint Andes mints
Prepare light metal cookie sheets by lining them with parchment paper.
With a large cookie scoop, scoop the dough onto the prepared cookie sheets.
With a flat bottom cup, press down on each cookie dough ball to slightly flatten it.
Place the cookies in the oven and bake for 8-10 minutes until the cookies looks slightly dull.
Remove and allow the cookies to set on the pan for 5-10 minutes before removing and allowing them to fully cool.
Peppermint Frosting
In the bowl of a standing mixer, add 1 cup of room-temperature butter and 3 cups of powdered sugar. Mix until combined.
Add 1/2 tsp of peppermint extract and 1 tbsp of heavy whipping cream. Mix until combined, then turn the mixer up to high and whip for 1-2 minutes.
Fold in the 1/2 cup of crushed candy cane
Assemble
Scoop frosting onto each cookie and spread out with an off-set spatula.