Name a Louisiana cocktail containing Bourbon and Pernod?

The cocktail you're looking for is the Sazerac. It's a classic New Orleans drink made with:

* Rye or Bourbon whiskey

* Absinthe (Pernod is a common brand of absinthe)

* Sugar

* Peychaud's Bitters

The Sazerac is typically served in a chilled, old-fashioned glass with a lemon twist.