Set aside 1 tablespoon of chocolate cookie crumbs for garnish, or as desired. Combine remaining cookie crumbs with butter in a bowl; press into the bottom of a deep-dish 9-inch pie plate.
Heat marshmallows and milk in a large saucepan over low heat, whisking until marshmallows melt. Marshmallows will inflate and rise to the top of the pan as they heat; stir constantly to avoid boiling over. Cool marshmallow mixture to room temperature. Stir creme de menthe and creme de cacao liqueurs into mixture.
Set pot into a large bowl of ice and chill until marshmallow mixture is cold and syrupy, at least 30 minutes. Gently fold whipped cream into marshmallow mixture. Pour filling into prepared cookie crust. Chill overnight. Sprinkle with reserved cookie crumbs.