Fill a rocks glass with ice and allow to chill. In a cocktail shaker, add sugar cubes, bitters, and rye whiskey. Muddle sugar cubes. Top with ice and stir for 30 seconds.
Empty ice from rocks glass. Add absinthe to glass and swirl to coat. Pour out absinthe. Strain cocktail into absinthe-lined glass. Twist lemon peel to release the oils. Rub lip of glass with the peel and drop into cocktail.