Just inside the entrance to an Italian restaurant on a recent afternoon in the historic St. George neighborhood on Staten Island, the smell of soy and ponzu masked that of onions and garlic.

The source? A Japanese woman had taken over the kitchen to make gyoza and shrimp dumpling soup.

“The dumplings are good!” said a customer at a table of seven, sounding surprised.

The next night, however, the dumplings would not be there.

At Enoteca Maria, an “Italian” restaurant on Hyatt Street, half of the menu changes daily. The fixed half is Italian; the rest is left for rotating cuisines from all over the world. And the people calling the shots are not professional chefs; they are grandmothers.

Each night, a “nonna” (Italian for grandmother) from a different country designs a fresh menu, honoring her native cuisine.

Friday was Sri Lanka; Thursday, the Philippines; Tuesday, Armenia.

A man eating at the bar asked about the next Sunday menu: Russia.

Mary McLaughlin, 68, had cod and the gyoza. The man sitting next to her had lasagna. Ms. McLaughlin, who traveled 32 miles from Floral Park, on Long Island, to dine at the restaurant, said she liked the idea of rotating chefs who knew their way around a truly home-cooked meal.

An article in some editions last Sunday about Enoteca Maria, a restaurant in Staten Island that employs grandmothers as chefs, misstated the given name of a customer. She is Concetta Smith, not Toncetta.

A version of this article appears in print on March 5, 2017, Section MB, Page 1 of the New York edition with the headline: International House of Grandmas.