I first had this cocktail in Boston at Legal Seafood and was amazed. I got their recipe and I tweaked it to my liking, and here is my tried-and-true perfect Vieux Carre:
.75oz Rye Whiskey (George Dickel is fine, but try different ones to find your favorite)
.75oz Pierre Ferrand Ambre cognac
.40oz Carpano Antica Formula vermouth (Just under the 1/2oz mark)
.20oz Benedictine (Just under the 1/4oz mark)
2 dashes Angostura Bitters
2 dashes Peychaud's Bitters
Pour all of the above into a cocktail shaker, add crushed ice, stir with a barspoon at least 50 times, then strain into a rocks glass (preferably with one of those oversized ice cubes that won't melt).
Finally, add a lemon twist: Cut a small piece from the peel of a lemon, squeeze the oils into the drink (from the peel), then rub it on the rim of the glass)
Perfect! Feel free to mess around with the measurements to find your perfect cocktail. For me, the vermouth was coming through too much so I had to reduce that, and the Benedictine is very nice, but was a hair too sweet so I reduced it just slightly. Now I've had plenty of these and this is my absolute favorite recipe for my favorite drink.