Combine crumbs and butter in a small bowl; stir with a fork until moist. Press into bottom of a 9-inch springform pan. Chill.
Combine milk and marshmallow creme in a microwave-safe bowl; microwave at HIGH 1 minute, stirring once. Add crème de menthe, crème de cacao, and whipped topping, stirring until blended. Spread ice cream into prepared pan; top with marshmallow mixture. Freeze at least 6 hours. Drizzle with chocolate syrup before serving.