In the bowl of a stand mixer, whip the cream, on medium speed, until stiff peaks form. Set aside.
In a separate large bowl, stir together the condensed milk with the creme de menthe and creme de cocoa until well combined. Mix in the cookie pieces, reserving a few for the top. Gently fold in the whipped cream, until mostly incorporated and then spread the mixture evenly in an 8” x 8” freezer-safe baking pan.
Lastly, 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 (Because you can never have enough right?!), cover with plastic wrap and pop into the freezer for at least 5 hours, but preferably overnight
Serve as is, or feel free to top the ice cream with extra cookie pieces, chocolate sprinkles or chocolate chips, a little fresh mint or even some whipped cream and hot fudge sauce.
Side note: If you’d prefer to make this without alcohol, simply skip the creme de cocoa, replace the creme de menthe with a few drops of peppermint extract (peppermint extract is very strong so add it according to your taste preferences but I recommend 1-1 ½ teaspoons) and, if you still want your ice cream to have the green color, don’t forget a few drops of green food coloring