Make Crust: In a food processor, pulse Oreos until they form coarse crumbs. Add butter and blend until completely combined.
Press crumb mixture into bottom and evenly up sides of a 9″ pie dish. (Try to make crust about 1/8″-thick evenly all around.) Refrigerate at least 1 hour before adding filling.
Make Filling: Using a stand mixer with the whisk attachment, beat heavy cream until stiff peaks form. Transfer to a bowl.
To bowl of stand mixer, add cream cheese and beat on medium-high speed, 2 minutes. Add powdered sugar and food coloring and mix on low until smooth. Add vanilla and peppermint extracts and mix until combined. With a rubber spatula, fold whipped cream into cream cheese mixture, then fold in mini chocolate chips and chopped Andes mints.
Pour filling into prepared crust and smooth top. Sprinkle with more mini chocolate chips and chopped Andes and drizzle with chocolate. Refrigerate until firm, 5 to 6 hours.