Today Stewart serves on a committee that oversees the city's reveillon menus to make sure the chefs are using ingredients that would have been used in the early days.
"The idea is to keep it as traditional as possible but leaving some room for creativity with the ingredients," he said.
At The Grill Room at the Windsor Court, executive chef Kristin Butterworth — a recent transplant to New Orleans from Pittsburgh — researched for months before presenting her first reveillon menu of braised pork belly with Gulf shrimp and white beans, local snapper with fennel and crawfish sausage and tenderloin with winter squash.
"When I delved into it and started to look at the history and the tradition of this meal, it was so amazing and so interesting to me," she said. "I wanted to get it right."
Even the salad took months of preparation, she said. Her winter greens are served with baby beets and squab prosciutto that Butterworth and her team cured in-house with salt, sugar, peppercorn and other spices over the past two months.
"A lot of love went into this menu," she said.
Select restaurants offer a wine-pairing option with each reveillon course and cafe brulot — a traditional New Orleans holiday beverage of strong coffee infused with strips of citrus, sugar, cloves, cinnamon and cognac or brandy.
Stewart, like other traditionalists, says the hot, thick and sweet concoction is "the perfect cap to a big holiday meal."
Some restaurants serve the beverage flaming tableside for added drama.
Though New Orleans is just about the only U.S. city that celebrates reveillon, the tradition is still alive in France, parts of Canada and other French-speaking places where it is a long dinner and celebration held on the evenings preceding Christmas Day and New Year's Day.
Reveillon is also celebrated in Brazil and Portugal on New Year's Eve. Some two million people flock to the shores of Copacabana beach in Rio de Janeiro for music and fireworks.
"It's like what we do in Times Square but on a larger scale and on the beach," said Michelle Sobhraj, spokeswoman for a New York-based marketing company that promotes Brazilian tourism.
In Brazil, revelers don outfits in the color that symbolizes their wishes for the New Year, such as red for romance and white for peace and luck. Many carry pockets full of money for continued prosperity and a bay leaf in their wallets for luck.
New Orleans Reveillon Dinners, http://www.neworleansonline.com/holiday/
The Historic New Orleans Collection, http://www.hnoc.org/