Spread the marshmallows out on a parchment-lined baking sheet and broil in the oven until the tops are golden brown. Make sure to watch your marshmallows while they are in the oven so that they do not burn.
In a blender, combine together heavy cream, sweetened condensed milk, milk, chocolate syrup, vanilla extract, and the toasted marshmallows.
Fill the ice cream maker with the mixture. While the machine is running add in the crushed graham crackers. Allow the machine to run for 15-20 minutes.
Serve or freeze for later. Ice cream will be very soft right out of the machine.
When serving, top with your favorite garnishments like chocolate shavings, chocolate syrup, crushed graham cracker, and/or marshmallows.
Tip: When making ice cream be sure to keep your cold ingredients in the fridge and your frozen ice cream insert in the freezer until you are ready to use.