Throw the cookies and melted butter into a food processor and pulverize. (Or, if you have some aggression or energy to expend, you can crush them in a large resealable plastic bag using a rolling pin!) Set a small handful of crumbs aside to sprinkle over the finished pie. Pour the rest into a pie pan and press into the bottom and up the sides of the pan. Set aside.
Heat the marshmallow and half-and-half in a saucepan over low heat, stirring constantly. As soon as it's all melted and combined, place the saucepan in a bowl of ice to cool down quickly. (Stirring occasionally will hasten this process.) Once cool, add the creme de menthe and creme de cacao. Taste and add more creme de menthe if needed. Add the green food coloring if using.
In a mixing bowl, beat the cream until stiff. Pour the cold marshmallow mixture into the whipped cream and fold together gently. Pour the filling into the chocolate crust. Sprinkle over the reserved cookie crumbs.
Freeze until very firm, about 2 hours. Remove from the freezer 10 minutes or so before you want to slice and serve.