Combine the marshmallows and milk in a large saucepan. Cook over medium heat, stirring constantly, until the marshmallows have melted. Remove from the heat and immediately stir in the toffee pieces, Let the toffee pieces melt slightly, then transfer to the refrigerator until thickened, but not set, 15-20 minutes.
Beat the whipping cream to stiff peaks. Stir about one-fourth of the cream into the marshmallow mixture. Fold in the remaining cream. Spread the mixture into the pie crust. Refrigerate until fully set, about 3 hours.
Serve drizzled with chocolate sauce and sprinkled with additional toffee pieces.