A quick heads-up before diving into the story: I've set aside for you a complete shopping list of every ingredient you'll need so you can recreate this classic at home. Here's the tale.
The Vieux Carré ("Old Square", the French name of the New Orleans French Quarter) was created in 1938 by bartender Walter Bergeron at the Carousel Bar of the Hotel Monteleone, the famous rotating-bar hotel in the heart of the Vieux Carré. Bergeron wanted to create a drink that would capture the multi-ethnic soul of New Orleans: the French, the Spanish, the American and the Creole.
He mixed rye whiskey (American), cognac (French), sweet vermouth (Italian, for the Spanish influence), Bénédictine (monastic French) and Peychaud's Bitters (Creole). The result is a liquid geography lesson, so complete that the IBA recognizes it as a modern classic. The Hotel Monteleone still serves it at the same rotating bar, now a UN-listed literary landmark frequented over the decades by Faulkner, Hemingway and Truman Capote.
To recreate this one with the right style, tools matter as much as the recipe. I use and recommend a complete barman kit like this set on Amazon, which covers every essential tool at a very reasonable price. For a more serious setup, a professional cocktail bar station keeps bottles, glasses and tools organized and close at hand, instantly upgrading the whole experience.