In a large mixing bowl, whip the heavy cream on medium speed until stiff peaks form. Be careful not to overwhip. Set aside.
In another large bowl, combine the condensed milk, crème de menthe liqueur, and crème de cacao liqueur. Mix until well combined.
Gently fold in the broken chocolate sandwich cookies until evenly distributed throughout the mixture, but reserve a few for the top.
Pour the ice cream mixture into a 8” x 8” freezer-safe baking pan. Smooth the top with a spatula.
Spoon the marshmallow fluff in large dollops across the top of the cream mixture. Use a knife or spoon to gently swirl it into the rest of the mixture.
Top with a few additional cookie pieces.
Cover the container with plastic wrap or a lid and place it in the freezer. Allow the ice cream to freeze for at least 5 hours, or preferably overnight, until firm.
When ready to serve, remove the ice cream from the freezer and let it sit at room temperature for a few minutes to soften slightly. Scoop the grasshopper pie ice cream into bowls or cones. Feel free to garnish with extra cookie pieces, chocolate sprinkles, chocolate chips, chocolate shavings, mint sprigs, whipped cream, chocolate syrup, and/or hot fudge syrup.