Mr. Brown says he had become enamored with the internet boom sweeping the U.S. in the late ’90s and jumped to an online travel portal. The startup soon flopped, taking his savings with it.

“This was that big failure moment,” said Mr. Brown, who was in his early 30s at the time and had two young children. “I had to think about what I want to be doing in my career—what I’m really good at doing.”

Mr. Brown, who is now 55 years old, narrowed his focus to the hospitality business and working with established companies. He consulted for McKinsey & Co. before becoming

Expedia Group Inc.’s

North American president, helping to devise strategy at the travel-booking site.

Mr. Brown’s next position as president of global brands and shared services at

Hilton

Worldwide Holdings Inc. helped him gain experience in bringing together disparate brands under one banner.

Blackstone Group

had just bought Hilton, and he learned more about private-equity sponsors of companies, he said. In 2013, private-equity firm Roark Capital Group tried to recruit Mr. Brown to lead its Arby’s investment. He initially turned them down.

“I went, ‘That looks hard,’ ” Mr. Brown said. Roark convinced him to take the leap and Mr. Brown oversaw improving sales. Mr. Brown grew close with Roark founder

Neal Aronson,

and the two helped sketch out a strategy to acquire other midsize restaurant brands to fold together. In 2018, they founded Inspire Brands Inc., with Mr. Brown serving as chief executive and Roark providing financial sponsorship. The Atlanta-based company now owns around 32,000 restaurant locations doing $30 billion in annual sales under the Arby’s, Buffalo Wild Wings, Sonic Drive-In, Jimmy John’s, Dunkin’ and Baskin-Robbins chains. Franchisees operate most locations.

Restaurants this year are facing growing costs and an uncertain outlook for consumer demand, and Mr. Brown said he worries about the economy further cooling next year. Same-store sales this year for some of his brands are weaker compared with 2021, when they experienced big demand surges as America reopened from pandemic closures. But Mr. Brown is bullish on Inspire’s multibrand approach.

“People went into this situation in a unique environment we’ve never seen before,” he said. “I’m feeling good about the portfolio and how we are competing.”

Here are four of his most trusted advisers:

Adm. Sandy Winnefeld

Chairman, President’s Intelligence Advisory Board

Mr. Brown said he met Mr. Winnefeld years ago at a gathering for Georgia Tech alumni, where both men were sitting around a campfire late one night. Mr. Winnefeld shared stories about his time with the U.S. Navy, where he eventually served as the vice chairman of the Joint Chiefs of Staff. Mr. Brown was struck by the officer’s ability to lead through complex and lengthy challenges.

Since then, Mr. Brown has turned to Adm. Winnefeld, now retired from the U.S. Navy, for guidance on how to lead teams, calling him for advice on how to keep employees aligned with the company’s strategy.

“He’s just that guy on the other end of the phone,” Mr. Brown said.

Mr. Brown has tapped Adm. Winnefeld to speak with Inspire senior leaders and restaurant franchisees. When the Covid-19 pandemic struck, Mr. Winnefeld talked to workers virtually about how to keep moving through a crisis, Mr. Brown said.

Barry Diller

Chairman and Senior Executive of

and Expedia Group

Mr. Brown still recalls the moment when he was on a train in London in 2005 and got a call from Mr. Diller, who was trying to recruit him to his Expedia travel site from McKinsey.

“It wasn’t a going-through-the-motions call. He genuinely cared whether I joined that company,” said Mr. Brown, who tries to emulate that approach with Inspire employees.

Mr. Diller’s pitch worked, and after he took the Expedia job, Mr. Brown said he learned from the top executive about how to negotiate. One central tenet: Never bluff, unless you are willing to accept the consequences. Otherwise, Mr. Brown said, “you’ve lost your leverage forever with them, and you’ve lost credibility in the relationship.”

Christopher Nassetta

President and CEO, Hilton

Mr. Nassetta was one of the first people Mr. Brown called for advice on how to deal with the pandemic’s impact on his restaurants’ operations. Mr. Brown’s former boss navigated the 2008 financial meltdown, and Mr. Nassetta advised him to shore up Inspire’s balance sheet and have cash on hand, he said.

“He just had his plan right and that helped in executing it,” Mr. Brown said.

Mr. Brown has also turned to Mr. Nassetta for guidance about knitting together brands under one company, a process he’s now engaged in at Inspire across its restaurants. He was initially skeptical about the importance of brand culture at Hilton—which owns Hampton Inn, DoubleTree and Embassy Suites—but Mr. Nassetta showed him how much it can matter, Mr. Brown said.

When a situation comes up for an employee, having a strong sense of the brand’s standards matters more than a detailed operating manual, Mr. Brown ecalled learning under Mr. Narsetta.

“That’s the only glue that can hold it together,” he said.

Melissa Coley

Executive Assistant to the CEO, Inspire Brands

Ms. Coley was hired as Mr. Brown’s assistant soon after he joined Arby’s, and within months she was diagnosed with non-Hodgkin lymphoma. She asked to continue working as much as possible during her treatment. About 18 months after successful treatment of the lymphoma, Ms. Coley was later diagnosed with leukemia.

Mr. Brown said Ms. Coley’s attitude and work ethic often inspires him, particularly when he’s in a funk.

“I have those moments where something will be going wrong and I start feeling a little sorry for myself,” he said. “And I walk out the door and I’ll be like, ‘Snap back out of it Paul. Good God.’ ”

Write to Heather Haddon at heather.haddon@wsj.com