Place melted butter in a small shallow dish that is a little larger than the rim of your mug. Place crushed graham crackers in another dish of the same size. Flip mugs upside-down and dip the rims first in melted butter then in the crushed graham crackers.
Break the chocolate into pieces and place one-half bar in each of the 4 mugs. Heat milk to a simmer and then carefully pour 1 cup into each mug over the chocolate. Set aside.
Place marshmallows on a parchment-lined baking sheet. Place under the broiler on low heat. Watch them toast and then remove from oven.
Stir hot milk mixture to distribute melted chocolate. Top each mug with 2-3 toasted marshmallows and drizzle with chocolate syrup.