Line a 9 x 13-inch baking pan with parchment paper (or foil). Allowing parchment paper to run up along the sides of the pan. Set aside.
In a large bowl, combine ground graham crackers and melted butter. Transfer mixture to prepared baking pan and press into an even layer along the bottom of the pan.
Pour cold heavy cream, condensed milk, and cocoa powder into a large bowl. Using a hand mixer, whip mixture to stiff peaks. Fold in chocolate chips.
Spread chocolate ice cream mixture over graham cracker layer. Place marshmallows on top of ice cream. Cover baking pan with plastic wrap. Freeze for at least 3 hours until ice cream has set up. Overnight is best.
Gently remove s'mores ice cream bar from baking pan by lifting from parchment overhang. Place on a cutting board and cut into bars using marshmallows as guides.*
Brown the marshmallows tops with a kitchen torch. Enjoy immediately!