Chill a martini or coupe glass in the fridge or freezer so the drink stays extra cold and creamy.
Pour a little chocolate syrup onto a small plate, dip the rim of the chilled glass into the syrup, then press it into graham cracker crumbs to create a graham cracker rim.
Fill a cocktail shaker with ice.
Add the marshmallow or vanilla vodka, chocolate liqueur or Irish cream, and half-and-half or heavy cream to the shaker.
Pour in the chocolate syrup or chocolate sauce.
Shake well for about 15 seconds, until the outside of the shaker feels cold and the mixture is smooth and frothy.
Strain the cocktail into the prepared, graham-cracker-rimmed martini glass.
Toast a jumbo marshmallow with a kitchen torch or lighter until golden and lightly charred, then carefully place it on top of the drink using tongs.
If desired, drizzle a little extra chocolate sauce over the top or add a small spoonful of marshmallow fluff and a sprinkle of crushed graham crackers.