Snackboxe Bistro in Atlanta, was a child in a small town in east-central Alabama, where her family settled after fleeing Laos as refugees. They fermented their own fish sauce, and her father made a weekly trek to Atlanta to pick up lemongrass and galangal at the international farmers’ market.

The essayist Jay Caspian Kang has described Americans of Asian descent as “the loneliest Americans.” Even after the government eased restrictions on immigration from Asia in 1965, being an Asian-American outside major cities often meant living in isolation — the only Asian family in town, the only Asian child at school. A grocery store could be a lifeline.

When the writer Jenny Han, 40, was growing up in Richmond, Va., in the ’90s, her family shopped at the hole-in-the-wall Oriental Market, run by a woman at their church. It was the one place where they could load up on toasted sesame oil and rent VHS tapes of Korean dramas, waiting to pounce when someone returned a missing episode.

A few states away, the future YouTube cooking star Emily Kim — better known as Maangchi — was newly arrived in Columbia, Mo., with a stash of meju, bricks of dried soybean paste, hidden at the bottom of her bag. She was worried that in her new American home she wouldn’t be able to find such essentials.

Then she stumbled on a tiny shop, also called Oriental Market. One day the Korean woman at the counter invited her to stay for a bowl of soup her husband had just made.

“She was my friend,” Maangchi recalled.

Kim’s Convenience” might say, a sneak attack. Once Brian Kwon entered the office, he never left. “My father called it his ‘golden plan,’ after the fact,” he said ruefully. He is now a co-president, alongside his mother and his sister, Stacey, 33. (His father is the chief executive.)

For many non-Asian customers, H Mart is itself a sneak attack. On their first visit, they’re not actually looking for Asian ingredients; customer data shows that they’re drawn instead to the variety and freshness of more familiar produce, seafood and meat. Only later do they start examining bags of Jolly Pong, a sweet puffed-wheat snack, and red-foil-capped bottles of Yakult — a fermented milk drink that sold out after it appeared in Ms. Han’s best-selling novel-turned-movie “To All The Boys I’ve Loved Before.”

To be welcoming to non-Koreans, H Mart puts up signs in English. At the same time, the younger Mr. Kwon said, “We don’t want to be the gentrified store.” So while some non-Asians recoil from the tanks of lobsters, the Kwons are committed to offering live seafood.

Sunday Family Hospitality Group, in San Francisco, remembers the H Mart of his youth in New Jersey as “just the Korean store” — a sanctuary for his parents, recent immigrants still not at ease in English. Everyone spoke Korean, and all that banchan was a relief: His mother would pack them in her cart for dinner, then pretend she’d made them herself.

Later, as a teenager, he started seeing his Chinese- and Filipino-American friends there, too, and then his non-Asian friends. Spurred by postings on social media, young patrons would line up to buy the latest snack sensation — “the snack aisle is notorious,” Mr. Hong said — like Haitai honey butter chips and Xiao Mei boba ice cream bars. (The current craze: Orion chocolate-churro-flavored snacks that look like baby turtles.)

In “Mister Jiu’s in Chinatown,” a new cookbook by the chef Brandon Jew and Tienlon Ho, Mr. Jew, 41, recalls Sunday mornings in San Francisco with his ying ying (paternal grandmother in Cantonese), taking three bus transfers to traverse the city, on a mission for fresh chicken — sometimes slaughtered on the spot — and ingredients like pea shoots and lotus leaves.

He still prefers “that Old World kind of shopping,” he said, from independent vendors, each with his own specialties and occasional grouchiness and eccentricities. But he knows that the proliferation of supermarkets like H Mart and 99 Ranch makes it easier for newcomers to Asian food to recreate his recipes.

“Access to those ingredients leads to a deeper understanding of the cuisine,” he said. “And that in turn can become a deeper understanding of a community and a culture.”

Chai Pani in Asheville, N.C., and Atlanta, feels that something is lost when you buy paneer and grass-fed ghee at a Whole Foods Market. You miss the cultural immersion, he says, “getting a dunk and having horizons broadened.”

“An Indian grocery is not just a convenience — it’s a temple,” he said. “You’re feeding the soul. Come in and pick up on the energy.”

In the TV special “Luda Can’t Cook,” which premiered in February, Mr. Irani takes the rapper Ludacris to Cherians, an Indian supermarket in Atlanta. Once Mr. Irani had to scrounge for spices like cumin and turmeric at health food stores; now, surrounded by burlap sacks stuffed with cardamom pods and dried green mango, he tells Ludacris, “This is my house.”

Min Jin Lee, 52, remembers how important H Mart was to people working in Manhattan’s Koreatown in the ’80s, when it was still called Han Ah Reum and “tiny, with almost no place to negotiate yourself through the aisles,” she said. (It has since moved across West 32nd Street to a larger space.) Her parents ran a jewelry wholesale business around the corner, and relied on the store for a cheap but substantial dosirak (lunch box) that came with cups of soup and rice.

She sees the modern incarnation of the store as a boon for second- and third-generation Korean Americans, including thousands of Korean-born adoptees raised by white American parents, who “want to find some sort of connection to the food of their families,” she said. “There aren’t gatekeepers to say who’s in or who’s out.”

BTS — anti-Asian sentiment is growing. With visibility comes risk.

For Ms. Lee, this makes H Mart a comfort. “I like going there because I feel good there,” she said. “In the context of hatred against my community, to see part of my culture being valued — it’s exceptional.”

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