Sazerac, the official cocktail of New Orleans, was originally made with Sazerac de Forge et Fils cognac. The phyloxera plague of the late 1800s that decimated the vineyards of Europe led to a scarcity of cognac and the use of the more readily available rye whiskey as the main ingredient of the Sazerac. Other whiskeys can and have been used, but rye has been the default spirit for over a century. While you might try a Sazerac made with brandy or bourbon, you must use Peychaud's bitters, not Angostrua or any of the others.
2 oz rye whiskey (the better the rye, the better the drink)
3-4 dashes Peychaud's bitters
1 sugar cube or ½ oz simple syrup
Splash of absinthe (or herbsaint, pernod, or Ricard)
Lemon peel for garnish
Fill an old-fashioned glass with ice and set aside. In a separate mixing glass place the sugar and bitters. If using a sugar cube add a splash of water and muddle until disolved. Add the rye and some ice and stir well. Empty the ice from the first glass and coat the inside with a splash or two of the absinthe, pouring out the excess. Strain the rye, sugar, and bitters mixture into the absinthe coated glass and add the twisted lemon peel.