For marshmallow and ginger syrup:
1 cup sugar
1 cup water
½ cup grated fresh ginger
For each cocktail:
1½ ounces vodka (or whiskey or rum)
1½ ounces marshmallow and ginger syrup
1 marshmallow, for garnish
To make the syrup: toast the marshmallows over dying embers until they are dark brown and melted inside. Put them into a heavy-bottomed pot and add the sugar and water. Slowly bring to a boil, stirring frequently to dissolve the sugar and the marshmallows. Once you reach a gentle boil, turn the heat down to a simmer and continue cooking and stirring until the marshmallows have dissolved.
Remove the syrup from the heat, stir in the ginger, and transfer to a heatproof container. Cover and allow to cool overnight. The next day, strain the syrup through a fine-mesh strainer lined with cheesecloth. The syrup will keep in a tightly sealed container in the fridge for at least 2 weeks.
To make the cocktail: in a tall glass filled with ice, add the vodka and syrup. Top with soda water and gently stir. Squeeze in lime wedges to taste. Stick your garnish marshmallow onto a long toothpick. Light it on fire, blow it out, then stick the toothpick into the cocktail, marshmallow side out of the drink, to garnish.