In a medium bowl, whisk together the flour, baking powder, and salt; set aside. (The mixture will look like wet sand.)
In the bowl of a stand mixer fitted with the paddle attachment, blend the sugar, cocoa powder, and vegetable oil on medium speed until well combined. Add the eggs and vanilla and mix until thoroughly combined.
Add the flour mixture to the wet ingredients and mix on medium speed until well combined. (The mixture will be thick, but will slowly fall from the paddle once lifted.)
Smooth the dough up the sides of the bowl (this is a great tip) to help the dough chill faster. Freeze 45 - 60 minutes or until firm enough to handle. During the last 20 minutes of chilling, place a rack in the middle of the oven and preheat the oven to 350℉.
Using a ½-inch ice cream scoop, scoop dough out and shape into 1-inch balls. Transfer to a baking sheet lined with parchment paper or a silicone baking mat, spacing them 2 inches apart.
Flatten dough balls about halfway (with greased hands or a cup). Bake in a preheated oven for 9-11 minutes (they should appear slightly under-baked). Meanwhile, unwrap chocolates.
Immediately after removing chocolates from the oven, gently press one Andes Mint into each cookie. Let rest about 5 minutes until softened, then spread over the cookie.
Chill to set faster or transfer to a wire rack and let set at room temperature. Enjoy!