Missing Grandma’s cooking? Nonnas of the World can help.

“Grandma” and “kitchen” must be among the most comforting words in any language. It has been decades since I last stood by the stove with my grandma, and I feel my heart bloom as Zoraida Benitez welcomes me behind a shining stainless steel counter in the kitchen of a tiny restaurant on New York’s Staten Island.

Ms. Benitez, who is from Paraguay, is one of the nonnas, Italian for “grandmas,” on duty today. We are going to prepare a traditional meal from her home country.

Since 2007, Enoteca Maria, also known as Nonnas of the World, has served Italian dishes and a changing menu of other global cuisines to patrons who are as hungry for a home-cooked meal as they are for a smile, and maybe a hug, from a nonna.

Around 30 nonnas rotate as chefs. The restaurant is open Fridays through Sundays, and anyone can sign up for a free cooking lesson.

Today, Nonna Zoraida points to an apron hanging on the wall and hands me a hairnet. She’s outfitted in chef’s whites with her name and a spray of delicate flowers embroidered on her toque.

“My sister made it for me,” she says, patting the design with her fingertips. Nonna Zoraida has supported herself as a cook since she arrived in New York City 52 years ago.

“I cooked for 50 years for the Episcopalian church,” she says, stirring a bowl of chopped corn and milk. “Weddings, funerals, christenings, everything,” she says. There are no measuring cups or spoons. “All this, I just make by [my] eyes,” she says.

Her sous-chef, Fida, outfitted in black, has prepped a huge pile of onions in a neat julienned stack for bistec encebollado con mandioca – a dish of seasoned beef with sautéed onions served with yuca. Next, he slices chicken for vori vori with chipa guasu, a traditional Paraguayan chicken soup with cornmeal dumplings and a side of cornbread. A comforting aroma swirls up from the bubbling pot.

Nonna Zoraida points to the bay leaf canister on the wall above her head. Fida is from Pakistan, and they communicate mainly by pantomiming.

“Yes, Nonna,” he says as he reaches for it.

Nonna Zoraida pulls out her smartphone to show me a photo. “See? I have a certificate,” she says, beaming. The photo shows a framed 2001 culinary arts diploma from the New York Restaurant School. A few years ago, she retired from the church kitchen. Her daughter suggested she join Enoteca Maria to stay busy.

Owner Jody Scaravella says a lot of the chefs who work here are in one phase of retirement or another. “Many are seniors who have lost their spouses, their kids have moved out, and they’re living alone,” he says. “That’s one of the benefits [the restaurant offers] to the community.”

The kitchen counter is filling up, and Nonna Zoraida clears room for a large bowl where she is cracking eggs. She hands me an immersion blender and instructs me to beat the whites. I struggle to find room for my elbows.

“I cooked in a kitchen smaller than this,” she says with a wink. “I made 300 empanadas from 5 a.m. to 2 p.m. every Saturday in my kitchen and sold them to help pay for my children’s schooling.”

Nonna Zoraida has five children and five grandchildren. But being a grandma is not a prerequisite for working at Enoteca Maria.

“There are three qualifications to cook here,” says Mr. Scaravella, sitting at a wooden table by the front window, his tiny wire-framed glasses reflecting the blue sky and clouds outside. “You have to be at least 50 years old. You have to be born in the country that you represent. And you have to be a good cook.”

Mr. Scaravella opened Enoteca Maria because he missed the matriarchs of his family. As a boy, his Italian grandmother took care of him while his parents worked, and he helped her shop for ingredients to prepare homey dishes.

When he bought the storefront on Staten Island in 2006 he just had an inkling of an idea: Fill the kitchen with nonnas. So he placed an ad in an Italian American newspaper looking for housewives who could cook regional Italian cuisine. The response was overwhelming.

“All these ladies showed up with their husbands, their kids, their grandkids, their neighbors. I had all these people in the house with plates of food, vying for my attention,” says Mr. Scaravella. There was even a representative from an artisanal cheese company with a suitcase full of cheese.

If it sounds like a scene from a movie, it will be. Netflix plans to release “Nonnas,” starring Vince Vaughn and Susan Sarandon, May 9. The movie is based on Mr. Scaravella and his army of cooking grandmas. He says Simon & Schuster also is planning a reissue of his 2015 book, “Nonna’s House,” tied to the movie.

Mr. Scaravella initially opened with just Italian nonnas but soon made a change to the lineup.

“You can’t have two Italian nonnas in the kitchen at the same time, because they’re very competitive,” he explains. “We went from Italian ladies to Nonnas of the World because people coming in were from every walk of life. It just made sense to feature everybody’s grandmother.”

As the Paraguayan dishes simmer in the kitchen, I sit down to order from the lunch menu, which features options from Japan and Italy. My selections include a fluffy feta dip with yogurt, fresh mint, and pistachios served with homemade flaxseed crackers; seasoned tomatoes with fresh mozzarella balls so creamy and light they could have floated away; and spinach lasagna. For dessert, homemade gelato in three flavors: coffee, vanilla, and berry cheesecake. It is all delicious.

A man sitting next to me orders the Italian classic capuzzelle, lamb’s head roasted with fresh herbs and vegetables. It arrives served in the skull. “I wanted to be adventurous,” he explains to his female companion, who grimaces.

More diners arrive, filling the tables backed up against the exposed brick wall and looking around expectantly to catch a glimpse of a nonna.

“One customer came up to me and they said that, you know, ‘What you do here is real,’” says Mr. Scaravella. “So that really hit the spot for me.”

Mr. Scaravella has big plans. He wants to launch a brand of global ingredients curated by the nonnas. He also wants to turn the business into a 501(c)(3) nonprofit, where people can make reservations and pay online before they come.

“I want to take the money out of this environment,” says Mr. Scaravella. “I don’t like it at the end of a meal, handing somebody a check for grandma cooking – it doesn’t feel right.”

Nonna Zoraida is hovering with a spoon over a plate of braised oxtail with a perfect mound of white rice when I lean over the counter to say goodbye. Her face brightens into a smile. She doesn’t say anything as I wave, she simply nods. But anyone who knows a grandma knows what that means: Come again soon.