There are a few versions of the story. In one, Carlos chopped a cheeseburger to fit a hero roll after running out of circular buns. Another holds that Yemeni workers came up with the sandwich along with Carlos, perhaps bringing some techniques from their home country. A third posits that Carlos had dental issues and was trying to make a burger easier to chew.

Sam Moslih, who works evenings at the bodega, said someone had seen the creation and asked Carlos to make one. “And,” he continued, “it just went from there.”

Fame

For years, the sandwich enjoyed a below-the-radar kind of renown, savored by those who grew up eating it at bodegas across the city, unknown to many others — and fetishized by a few.

Soon as I step out my building, they like I need that / Hajji’s for dinner, them chopped cheese I still eat that — The Harlem rapper Dave East in the song “Nino”

Usually costing $4 or $5, the sandwich has the qualities of what scientists call an emergent property — it is greater than the sum of its parts. Fans of the food say part of its appeal is that it is infinitely customizable.

“It’s not supposed to be a gourmet item,” said Anthony Ramirez II, a Bronx entrepreneur who owns a restaurant and bar, the Bronx Beer Hall, and the company FromTheBronx.com.

Mr. Ramirez said the sandwich was popular with students he used to work with. “You don’t go out of your way looking for it,” he said. “It’s an affordable option, and it’s hot and tasty.”

But in recent years, the sandwich has been finding a wider audience: a cameo in a Bronx-themed episode of Anthony Bourdain’s CNN show, “Parts Unknown”; a shout-out in a restaurant review in The New York Times; an in-depth look on a food blog run by Complex Media; and a growing volume of web features, music videos and social media chatter.

Whatever it was, the chopped cheese’s star was on the rise.

The Almonte Episode