Fill a double old fashioned glass with ice and a small amount of Absinthe (Herbsaint or Ricard). Stir the rum, sugar cane syrup and bitters in an ice filled shaker glass. Dump the ice from the old fashioned glass and rotate the glass to ensure that the rinse coats the entire inside of the glass. Strain into the glass. Twist lemon peel over the glass and discard (do not put the twist in the glass).