Finely crush the chocolate cookies in a food processor or blender. Mix in the melted butter until evenly combined. Press the mixture into the bottom and slightly up the sides of a 9-inch pie plate. Chill for at least 30 minutes.

In a double boiler, melt the marshmallows and milk together, stirring frequently until smooth. Remove from heat and stir in the chopped milk chocolate until melted and combined. Allow to cool to room temperature.

In a stand mixer fitted with the whisk attachment, beat the cold heavy cream on medium-high speed until stiff peaks form. Gently fold the whipped cream into the cooled chocolate mixture until fully combined.

Pour the marshmallow-chocolate filling into the prepared crust and smooth the top. Chill in the refrigerator for at least 2 hours before serving.

Before serving, garnish with additional whipped cream and chocolate shavings if desired.