Spread the graham cracker crumbs out on a small plate. It should be at least as wide as the rim of your glass.
Place a marshmallow on a small plate and microwave it for 10 seconds.
Run the rim of the glass through the softened marshmallow to coat the edge. Dip the rim into the graham cracker crumbs until coated. Set aside
Fill a cocktail shaker with ice. Pour in the vodka, chocolate liqueur, and half-n-half. Cover and shake vigorously until cold.
Drizzle chocolate syrup on the inside of the martini glass. Strain the martini into the glass.
Garnish with a marshmallow on the rim and enjoy.
Notes
Swap out for marshmallow-flavored vodka, or use 3/4-ounce of each for even more marshmallow flavor.
You can use regular Jet-Puffed marshmallows, chocolate marshmallows, or chocolate Stuffed Puffs. You want regular sized-marshmallows... not mini, jumbo, or the flat s'mores one.