Cream butter, sugar and brown sugar together. Add peppermint and mint, mix until combined. Mix in flour and salt. Fold in Andes Mints. Set aside.
Twist apart the Oreo's, and place on a baking sheet. It is OK if they break a little, you can use the cookie dough to help hold it together. Place 1-2 tsp of cookie dough on top of the side of the Oreo with the cream. Gently flip that over, and press down onto the side without the cream. Leave the side without the cream on the baking sheet to help prevent breaking.
Dip Oreo's into the melted chocolate. Garnish with crushed candy canes, if desired. Let the chocolate fully harden before serving.