Combine cookie crumbs, 1/4 cup granulated sugar, and melted butter in a bowl. Press the mixture firmly into the bottom and up the sides of a 9-inch pie plate. Freeze the crust for 15 minutes.
Beat the softened cream cheese until smooth. Gradually beat in the powdered sugar, 1/2 cup milk, and vanilla extract until the mixture is creamy. Fold in half of the thawed whipped topping. Spread this mixture evenly over the chilled crust.
In a separate bowl, whisk the instant chocolate pudding mix and 2 cups of cold milk until the mixture thickens, about 2 minutes. Spread the pudding mixture over the cream cheese layer.
Sprinkle the miniature marshmallows evenly over the pudding layer.
Cover the pie loosely with plastic wrap and chill for at least 4 hours, or until firm.
Before serving, top the pie with the remaining half of the thawed whipped topping. Slice and serve immediately.
Notes
You can substitute Oreo cookie crumbs for chocolate wafer crumbs for a different texture.
For a richer chocolate flavor, use dark chocolate pudding mix.
Keep the pie frozen until about 15 minutes before you plan to serve it for the best texture.