The traditional ritual for making a Sazerac cocktail uses two Old Fashioned glasses. One is chilled as described in this recipe and the other is used to stir the other ingredients (in lieu of a mixing glass). Also, the Sazerac came along before bartenders were using syrup so if you want to be strictly authentic you would use sugar. I use gum syrup in my recipe because the gum adds a richness and viscosity that I like in this drink.
If you don't have access to absinthe, you can substitute Herbsaint, Pernod or some other pastis. Be careful with the absinthe/Herbsaint/Pernod. You only want a hint of anise flavor in a Sazerac. Most recipes instruct you to pour out the excess but if you use the amount prescribed in this recipe you can just leave it in the glass (especially if it is good absinthe). I just use a dropper bottle to drip absinthe down the inside of the glass.
Old Overholt is traditionally used in the bars in New Orleans. It is a fine rye whiskey with a lot of character, but you can improve upon it by using Rittenhouse bonded rye, Wild Turkey rye, Van Winkle 13 Year Family Reserve rye or Sazerac 18 Year. If you use one of the better rye whiskeys, and you want to taste more of it, shorten your stirring time to 10-15 seconds. This allows more of the whiskey to shine through.
When you make this drink, the first thing to appreciate about it is the nose. The aroma. Bury your nose in the glass (you should be able to because the drink barely fills half of the glass). Inhale deeply. The lemon oil is predominant with hints of herbs and menthol from the bitters, and another layer of rye and oak from the whiskey. Very few things in this world smell better (the only thing I can think of right now is when the vegetables hit the hot roux in a gumbo). Lemon oil is a wonderful thing. It has no real taste, but instead has an ebullient and vigorous aroma that is much more complex than lemon juice alone.
You can tweak this recipe by using an orange twist along with the lemon. The two seem to set each other off. Enjoy this cocktail. It has been around for a long time, and it deserves another 200 years of adulation.