It all began for the Sazerac cocktail in the early 1800's when Antoine Amedee Peychaud mixed Cognac with his Peychaud bitters. In 1859 the drink was the signature drink of the Sazerac Coffee House in New Orleans, where it received its name. The exact reason for the substitution of rye whiskey for the Cognac is unclear, but the whiskey base is used today.
3 oz Rye Bourbon
3/4 oz Simple Syrup
Chill an old-fashioned glass by filling it with ice and letting it sit while preparing the rest of the drink.
In a separate mixing glass, muddle the simple syrup and Peychaud bitters together.
Add the rye whiskey and ice to the bitters
mixture and stir.
Discard the ice in the chilled glass and rinse it with absinthe by pouring a small amount into the glass, swirling it around and discarding the liquid.