In a bowl, mix together flour, cornstarch, salt, and baking soda. Set aside.
In the bowl of a stand mixer (or using a hand mixer), cream together butter and both sugars on medium speed until light and fluffy (2-3 minutes). With the mixer on low, add in egg and vanilla. Return mixer to medium and mix until incorporated. Scrape sides if needed.
With the mixer back on low, add dry ingredient mixture gradually until dough forms. Mix in Andes baking chips. Refrigerate dough for at least 30 minutes or up to 24 hours. Preheat oven to 350°F. Prepare baking sheets by lining with parchment paper or Silpat; set aside.
Form balls from approximately 1 1/2 tablespoons of dough. Place on baking sheet (I did 8 at a time, they do spread a bit). Bake for 11-13 minutes or until edges are just barely golden. Remove from oven and let cool for a couple of minutes on baking sheet before removing and placing on wire rack to finish cooling. Store in airtight container.
Video
Notes
An alternative is to replace the Andes mint chips with an equal amount of chopped Andes mint candies.