Here's when and where Chituari army in New York, Iron Man (Robert Downey Jr.) proposed that they check out the shawarma t he spotted while fending off the alien beings. Given the genius billionaire's near-death experience hauling a nuclear bomb to outer space, his teammates decided to indulge him.
As iconic as the post-credits scene already is, the story about how it came about makes it all the more interesting. The Avengers shawarma scene wasn't part of the original plan for the movie, it was born out of Downey perpetually wanting to improve his lines. So while Tony's dialog after crashing back to Earth was supposed to be short and straightforward, Downey Jr. decided to improvise, commenting on how he and the rest of the team should try the shawarma t he spotted during the battle. This was when Whedon and Marvel Studios realized that it might be a great idea to give an otherwise obscure line some payoff.
The cast didn't have time to film it before doing additional work after The Avengers' press conference, piquing the interest of fans and reporters who at that time were clueless what the additional shooting is for. While the famed scene was set in New York, the cast shot it in L.A. in at Elat Burger/Shalom Grill on W Pico Boulevard. Marvel Studios president Kevin Feige got everything all set-up after they spotted the location about three blocks away from the team's hotel, allowing them to quickly go in and out of there to continue with their junket interviews.
With the logistics all ironed out, there was just one more issue that the cast and crew faced for filming the shawarma scene. Since it'd been a while after they finished principal photography for The Avengers, Chris Evans was already sporting a full facial hair. They couldn't simply get rid of it as it was for his role as Curtis Everett in Bong Joon Ho's 2013 sci-fi movie, why Captain America wasn't eating in the shawarma scene.
While it took Marvel Studios extra work to add the shawarma post-credits scene for The Avengers, it's ultimately worth it. As previously mentioned, it's one of the best stingers they've had thus far as it simply showed the heroes eating and exhausted after battle. Scenes like this ground their characters, making them more relatable to fans which really what fuels the MCU.