For the root beer syrup:
To make the root beer syrup, reduce root beer over medium heat in a small saucepan and then reconstitute it with water until it's 2 parts root beer to 1 part water.
For the cocktail:
Combine root beer syrup, rye, and bitters in a glass with ice and stir for about 25 seconds. Rinse a rocks glass with absinthe, then strain the rye mixture into the glass.
Flame a twist of lemon over the drink, then discard.