Above all, there’s the cartoon mouse — also called Mickey, and indistinguishable from Mickey Mouse — whose iconic circular ears adorn the gates of the company’s factory, its trucks and a mascot in heavy demand at Paraguayan weddings.

But don’t get it twisted, said Viviana Blasco, 51, sitting in the capital, Asunción, among Mickey-branded stationery, T-shirts, and coffee cups.

There’s “the Disney Mickey,” said Ms. Blasco, one of five siblings who run the business, and “the Paraguayan Mickey, our Mickey.”

Still, if the Paraguayan Mickey seems remarkably similar to the Disney one, it may not be entirely a coincidence.

Paraguayans are notoriously creative — some would say light-fingered — when it comes to intellectual property.

Factories churn out knockoff Nike, Lacoste, and Adidas clothing. Paraguay’s educational authorities warned last year that Harvard University Paraguay — in Ciudad del Este, the country’s second-largest city and a counterfeiting hot spot — was awarding bogus medical degrees. (The school has no connection to the more famous Harvard.)

The map highlights Paraguay’s capital city of Asunción, in the southwestern part of the country, as well as the southeastern city of Ciudad del Este, near the Brazilian border. It also locates the northwestern Chaco region of Paraguay.

Paraguay ranks 86th out of 125 countries in an index compiled by the Property Rights Alliance, a research institute based in Washington, scoring 1.7 out of 10 for copyright protection.

But Mickey, the Blasco family enterprise, has survived multiple legal challenges leveled by Disney.

It is also a remarkably beloved institution that speaks to Paraguay’s peculiar history, gastronomy and national identity.

The Mickey saga began, Ms. Blasco said, in 1935.

Paraguay had just endured a deadly conflict with Bolivia over the Chaco, a tangle of sun-baked scrub. An earlier conflagration, the War of the Triple Alliance (1864-70), had seen Argentina, Brazil and Uruguay wipe out half of Paraguay’s population.

It was still reeling from both.

Ms. Blasco’s grandfather, Pascual, the son of Italian immigrants, saw an opportunity to spread some joy — and turn a profit. He opened a tiny shop selling fruit and homemade gelato. It was called Mickey.

Exactly where the idea came from, said Ms. Blasco, remains “something of a mystery.”

But Pascual, she said, often vacationed in Buenos Aires — Argentina’s cosmopolitan capital, known for movie theaters showing international films. Mickey Mouse was making his silver-screen debut, including in “The Gallopin’ Gaucho” (1928).

“On one of his trips, he must have seen the famous mouse,” Ms. Blasco said.

Whatever its origins, Mickey was a hit. A few years later, Pascual opened the Mickey Ice Cream Parlor, Café and Confectioners.

By 1969, Mickey was selling rice, sugar and baking soda in packages now decorated with the eponymous mouse. In 1978, the business moved to a factory topped by a 62-meter illuminated Christmas tree.

Ms. Blasco denied that her family had appropriated Disney’s property.

“We didn’t take it, we built a brand over many years. Mickey grew in parallel to Walt Disney,” Ms. Blasco said, becoming “deeply implanted in Paraguayan culture.”

That affinity was evident at several stores that stock Mickey products in Luque, a working-class suburb of Asunción.

The Mickey mascot was taking photos with fans, including Lilian Pavón, 54, a pediatric nurse. “I’m a fanatic of Mickey products,” she said, praising, in particular, the company’s breadcrumbs and oregano.

But her feelings for the 7-foot felt rodent go beyond condiments, she added, as Mickey bumped fists with shoppers and distributed ring-shaped biscuits called chipa.

As children, she said, she and her friends hoarded Mickey Mouse pencil cases, notebooks and stickers. They dreamed of visiting Disneyland or Walt Disney World. But the cost of flying to Anaheim or Orlando made the pilgrimage “impossible,” even as an adult, Ms. Pavón said.

“I’m happy just to see Mickey in places like this,” she added, standing in the chilled meats aisle of El Cacique, a budget supermarket.

Mickey resonates with Paraguayans’ sense of nostalgia, said Euge Aquino, a TV chef and social media influencer who uses its ingredients to make comfort food like pastel mandi’o (yuca and beef empanadas).

Paraguay is not known for its haute cuisine, she admitted.

It’s flat, hot, and a long way from foreign foodie trends.

“Our climate is pretty difficult,” Ms. Aquino, 41 said, “so you cultivate and eat whatever grows.”

What grows is mainly yuca or cassava and corn, which is sacred to the native Guaraní people. But what local dishes lack in pizazz, she said, they make up for in flavor and meaning.

Paraguayans still knead yuca starch and milled corn to make chipa during Holy Week. They infuse their yerba mate with fragrant herbs like boldo, burro, and begonias. They stuff their soups, stews and casseroles with aniseed, saffron, cloves, nutmeg, paprika and cilantro, all purveyed by Mickey in serving-size sachets.

“A moment, a taste, an aroma is a memory,’’ said Ms. Aquino, as a sopa paraguaya — a spongy “soup” made with Mickey corn flour — turned golden-brown in her oven. “And that memory can generate so many emotions. It’s your mom’s or your grandmother’s cooking.’’

Mickey’s popularity, she said, also has a lot to do with the mascot handing out candy outside the factory gates every Christmas: a tradition dating back to 1983.

Ms Aquino recalled feeling goose bumps as she waited outside the factory during the annual festivity in the early 1990s.

“There was no social media, there were no cellphones, there was nothing,” Ms. Aquino said. “Then suddenly Mickey comes along, and you’re like, ‘Wow!’ It was madness.”

“He’s a rock star,” she said.

By now, a “peaceful coexistence” reigns between Mickey and its United States doppelgänger, said Elba Rosa Britez, 72, the smaller company’s lawyer.

This truce was hard-won.

In 1991, Disney filed a trademark violation claim with Paraguay’s Ministry of Business and Industry that was rejected. The company then filed a lawsuit, but in 1995 a trademark tribunal ruled in Mickey’s favor.

Disney appealed again, taking the dispute to Paraguay’s highest court.

There, one judge agreed that Paraguayans could easily confuse the Disney Mickey and the Paraguayan Mickey.

But Disney didn’t reckon on a “legal loophole,” Ms Britez explained.

The Mickey trademark had been registered in Paraguay since at least 1956 — and Pascual’s descendants had since renewed it — without protest from the multinational.

In 1998, Paraguay’s Supreme Court issued its final ruling. Through decades of uninterrupted use, Mickey had acquired the right to be Mickey.

“I jumped for joy,” Ms Britez said.

Mickey’s legal immunity in Paraguay, Ms. Blasco acknowledged, might not extend to selling its products abroad. “We’ve never tried.”

The Paraguayan firm that represented Disney declined to comment. Disney officials did not respond to requests for comment.

During a recent national holiday, the man inside the Mickey mascot costume was warming up in an air-conditioned metal container inside the company’s factory that serves as his office.

Ms. Blasco asked The New York Times to withhold Mickey’s identity from the Paraguayan public to preserve some of the “magic” behind the mascot.

“Seeing the smiles on the kids’ faces is priceless,” the mascot said, before straightening his bow-tie and strolling out to his adoring public.

“Mickey!” they shouted, “Mickey!”

Mickey posed for photos, scattered sweets into strollers and passed popcorn through car windows to wide-eyed toddlers. Bus drivers honked their horns. A road-building crew waved. A worker leaned out of a garbage truck, pumped his fist and yelled: “Hey, Mickey!”

Some lining up to meet the mascot said Mickey’s David-vs-Goliath triumph against Disney filled them with national pride.