First, make the graham cracker milk. Place graham crackers in a small mixing bowl. Cover with the milk or half-and-half. (This will make more than you need, in case you want more cocktails!) Let it sit in the fridge for 4-8 hours. Strain out the graham crackers and pour it into a jar for use in cocktails.
In a zip-locking bag, place two graham crackers and seal the bag. Cover with a paper towel or tea towel and beat the bag with the back of a spoon until the graham crackers are crushed into crumbs. This can be as fine or crumbly as you wish, but coarse crumbs will work best. Pour crumbs onto a plate.
Pour a thin layer of chocolate syrup onto another plate.
Roll the outer edge of an old-fashioned glass in the chocolate syrup, then in graham cracker crumbs. If desired, spoon some chocolate syrup on the inside of the glass in a circular manner. Place glass in the freezer while you prepare your other ingredients to keep the chocolate from dripping.
To a cocktail shaker filled with ice, add marshmallow vodka, coffee liqueur and graham cracker milk. Shake until combined.
Add ice to the prepared old-fashioned glass, then pour in the liquid from the shaker.
Place a marshmallow on a skewer and give it a burst of flame from a kitchen blowtorch or lighter, until charred to your liking. Place on top of the cocktail glass for extra s’mores aroma. Enjoy!
The instructions are for how to mix one cocktail, but the Graham Cracker Milk makes as many as 15 more drinks.