The Vieux Carré is a classic cocktail that embodies the spirit of New Orleans with its complex and balanced flavors. The combination of brandy, rye whiskey, sweet vermouth, and Bénédictine liqueur creates a robust and sophisticated taste profile. The use of both Angostura bitters and Peychaud's bitters is a key characteristic of the Vieux Carré, adding depth and complexity to the cocktail. However, if you don't have Peychaud's bitters on hand, you can still enjoy a delicious Vieux Carré by using only Angostura bitters. Adjust the proportions of the ingredients to suit your taste preferences. Some variations may call for equal parts of each ingredient, while others may emphasize certain flavors more prominently.