Mix cookie crumbs and butter together in a bowl; press into a pie plate. Refrigerate pie crust until chilled, at least 30 minutes.
Heat marshmallows and milk together in a saucepan over medium-low heat until melted and smooth, 5 to 10 minutes.
Remove from heat and cool. Fold crushed peppermint candy into marshmallow mixture.
Beat cream in a glass or metal bowl using an electric mixer until medium peaks form. Lift your beater or whisk straight up: the tip of the peak formed should curl over slightly. Fold whipped cream into marshmallow mixture; pour into pie crust. Chill until set, at least 2 hours.
