Using a stand mixer or hand mixer, beat the butter and powdered sugar until creamy and add the vanilla. In a separate bowl, combine flour, salt, and cocoa powder, and mix. Gradually add the dry ingredients to the creamed butter mixture. Fold in the Andes mints along with the mini chocolate chips. Thoroughly mix until a dough forms.
Split the dough in half and form each half into a log about 12 inches in length and 1.5 in the round. Seal each log of dough with plastic kitchen wrap and then cut a slit in two empty paper towel rolls. Form the dough by pressing the rolls and store the cookie dough in there to prevent it from flattening. See this video for more instructions on this.
Refrigerate the dough for at least an hour, or you can freeze it for several months. If you freeze the dough, let it thaw for an hour before baking.
When ready to bake, preheat your oven to 350°. Slice the logs about ¼ inch in thickness, using a sharp knife. Arrange them at least an inch apart on a parchment paper-lined baking sheet and bake for 12 -15 minutes. Slide the parchment paper on a wire rack and along to cool completely.
To make the chocolate coating, using a microwave-safe bowl, combine the remaining chocolate chips with the vegetable oil. Microwave the chips and oil in 15-second intervals until smooth and creamy, making sure to stir between intervals.
Top the cookies with the chocolate coating and sprinkle the crushed candy canes on top of the soft coating. Gently press the pieces into the cookies and allow to completely cool. You can slide the parchment paper onto a rack in your refrigerator to speed up this process.
Add ½ teaspoon of mint extract to chocolate coating, for extra mint flavor.