Chill glass while stirring rye, peychaud's and simple syrup. You can also muddle sugar with the peychaud's and a little water if you don't have simple syrup on hand, some consider this more proper but I prefer the speed and consistency of simple syrup if I have it.
When you have good dilution of the stirred ingredients, set aside and spray the absinthe onto the chilled and empty glass. Express some oil from the orange, rim the glass with it and drop it in. I like to cut the twist right over the glass, spraying some extra orange oil in with the absinthe.
Now strain the stirred ingredients into the glass and serve.