In a chilled Old Fashioned glass, coat the inside of the glass by swirling with absinthe (discard any excess). Set aside.
To a mixing glass, add rye whiskey, simple syrup, and bitters. Fill mixing glass three-quarters of the way full with ice. Using a bar spoon, stir until mixture is fully combined and well chilled, about 30 seconds.
Strain into prepared glass. Pinch the lemon peel over the drink, rub the rim of the glass with the peel, and garnish with a lemon peel.
Absinthe: A highly-alcoholic anise-flavored spirit.
Whiskey: For the most authentic cocktail, choose Sazerac brand rye whiskey. Or, substitute Cognac (preferably Sazerac brand) or another brandy.
Simple syrup: To make it yourself, combine 1 cup water and 1 cup sugar in a small saucepan over medium heat. Stir until sugar is dissolved (do not boil). Remove from heat and cool before adding 1 tablespoon (or more to taste) to your cocktail shaker with the other ingredients. Store leftover simple syrup covered in the refrigerator for 3-4 weeks.
Bitters: Seek out Peychaud's bitters (a Sazerac brand) if possible. Angostura brand have a heavier flavor but will also work.
Yield: This recipe makes 1 cocktail.
Glassware: The Sazerac is traditionally made in an Old Fashioned glass, a 6-ounce to 10-ounce glass tumbler. Similar to a rocks glass or lowball glass, the Old Fashioned glass is decorated in the cut glass style.
Big batch: Sazeracs are best prepared one cocktail at a time.
Zazarack: Made with bourbon instead of rye whiskey (bourbon is sweeter in flavor and its mash must be made from at least 51% corn).