This is the quintessential New Orleans cocktail. If you want you can substitute the brandy for Whiskey and the absinthe for anise liqueur and this drink will still be good. Outside of New Orleans Whiskey was a popular substitute for brandy.
Once absinthe became illegal in the U.S. in 1912, bartenders began substituting it for anise liqueur. The Peychaud’s bitters on the other hand are what make this drink and cannot be replaced. Invented in the mid 1800s by a guy named Aaron Bird, this drink was unknown outside of New Orleans until the early 1900s.
The Sazerac is essentially the French influenced New Orleans variation of the Old Fashioned. Aaron named the drink after the brand of brandy/cognac (Sazerac-de-Forge et Fils) being imported by a local merchant that he first used to construct this drink.