Place the cookies in a food processor and pulverize. Pour in melted butter, and blend.
Place mixture in 10” pie plate that has been sprayed lightly with baking spray. Press crumbs into the bottom and up the sides of the pie pan, reserving a few extra to sprinkle over the pie later. Place in freezer while filling is made; at least 15 minutes.
In a saucepan, heat the marshmallows and half-and-half over low heat, stirring constantly. As soon as it is smooth and combined, pour into 2-cup glass measuring cup and place in bowl of ice to cool. Stirring helps speed up the process.
Once cool, add crème de menthe and crème de cacao. Taste and add more crème de menthe if needed. Add one or two drops of peppermint extract as needed for a stronger peppermint flavor.
In a mixing bowl, beat heavy cream until stiff. Pour the cooled marshmallow mixture into the whipped cream and fold together gently.
Pour the filling into the chocolate crust. Sprinkle the top with reserved cookie crumbs. Place the pie in freezer and freeze until very firm at least 2 hours or better overnight. Remove from freezer at least 10 minutes before serving.