In a large bowl or your stand mixer, mix butter, sugar, egg and vanilla. Stir in the flour, baking soda, and cream of tartar, just until combined. Add crushed Oreos and chopped Andes chips.
Preheat oven to 375º
Prepare sugar cookie dough
Stir in chopped oreas and andes peppermint baking chips
Drop dough by rounded tablespoons (using a cookie scoop, preferably) onto a parchment paper covered baking sheet.
Bake at 375 for about 10-12 minutes, or until edges are just starting to brown.
Cool on baking sheet for about 2 minutes before transferring to a colling rack. Store for up to a week in an air-tight container.