Prepare the chocolate syrup. In a small saucepan, over medium heat, combine heavy cream and butter. Bring the mixture to a simmer. Stir occasionally. Add both sugars and stir until dissolved.
Add chocolate pieces and salt to the mixture and cook at low heat until well combined. Remove from heat and allow to cool down for about 10 minutes.
Dip the rim of one mug in chocolate syrup and then dip it in graham cracker crumbs. Add to the mug the 1 tablespoon of chocolate syrup and 2 shots of espresso, stir. Froth the milk using a handheld frother. Carefully add the milk into the coffee mixture. Top with marshmallows and torch them until toasted.
Store the leftover chocolate syrup in an airtight container in the refrigerator. The syrup can be stored up to 1 week. Reheat before using.