Tom Brokaw, the legendary anchor and correspondent of NBC News, recently conducted an interview with the legendary David Letterman — gone from the air just over a full year, and has a white flowing beard to prove it. I spoke with Brokaw about the interview with the Great White Bearded One, along with a couple other matters.

Brokaw, by the way, was also recently accorded France’s highest honor — the Legion of Honor — “in recognition of his work on and advocacy for the accomplishments of World War II veterans.”

His interview with Letterman — Dave’s first on TV since leaving “The Late Show” last May — airs Sunday (“On Assignment,” 7 p.m. on NBC/4):

How did the Dave interview come together?

David and I have been personally close for a long, long time, and when he left NBC, we did this memorable profile up in Central Park. . . . We have a comfort level. Earlier this year, we exchanged emails from time to time, and I said, ‘When you are ready to come out again, I’m here.’

So you headed out to Indianapolis during the Indy 500 in late May for this? (Rahal Letterman Lanigan Racing, co-owned by Dave, Bobby Rahal and Mike Lanigan, is a very accomplished Indy car team, with 30 victories and three series championships over the years.)

advertisement | advertise on newsday

Yes, it was all in Indianapolis and spent the entire weekend. I hadn’t seen him since he left [and] my take-away is that he is in a very, very good place in his life. He said he thought it was going to be hard to not do the show every day and quickly realized that once Stephen [Colbert] took over, it kind of flowed out of his body, and was part of the past — not the present or future. He’s interested in a lot of other things. He went to India for National Geographic and is very involved with his Indy 500 team. I also helped steer him to Montana years ago, and he bought a ranch in a remote part of the state, and it’s become more and more important to his life. He’s learned to ride, he fishes. It’s a big place and a wilderness area. And then very much a big part of his life is [son] Harry. He wishes he had a brother or sister for him, but when I asked, he said that opportunity has passed ‘at my age.’

How did Dave characterize his departure? There has been a lingering sense among some that perhaps the departure was not on the happiest of terms with CBS, which did not consult him on Colbert. His reaction?

It was Dave being Dave. ‘Did they ask you [about the replacement]?’ He laughed, no — but they would never have done that. There’s no bitterness, no taking any kind of shot at CBS leadership. He said he thought Stephen was a good choice, but he wished that they had chosen a woman. There are a lot of women out there and it’s time to have one of them have those shows [he said]. I thought about it, too, later, and when I was talking with Sandra Bernhard recently, I asked her, ‘How many more are there like you besides Amy Schumer and Samantha Bee and the rest of the thriving class of really smart women comedians?’ She said, ‘A lot more than you’d realize.’

How’s Dave’s beard?

The beard was trimmed. He cut it back so that he didn’t look like Walt Whitman. . . . He said the reason he grew it is that from an early age, he had to shave twice a day, in the morning and then before air, and said, ‘I got so damn tired of doing it.’ Nobody else in the family likes it, and his son says it’s creepy. Everyone else complains, but Dave says, ‘it’s just dad.’

Now about you — how’s your health? (Brokaw was diagnosed with multiple myeloma — which weakens bones — in 2013, later producing a memorable “Dateline” story on his battle, “My Life Interrupted.”)

Under the circumstances, it’s as good as it can be. My cancer is in remission — not cured, and won’t be, unless they find some miracle cure. But it can be treated. It has affected my physique and had a lot more spinal damage, taking three inches from my height. But I’m riding my bike, swimming more, and doing the best I can under the circumstances. I don’t wake up thinking, ‘I’ve got cancer,’ but I do wake up knowing I have to take a fistful of pills, including for chemotherapy.

You’re going to Rio for the Olympics?

I am going to Brazil, to the Amazon, and Manaus, to do an essay. It’s a fascinating place, and then there are two conventions coming up. I won’t be one of the floor reporters running around.

Your take on what should be a pair of wild conventions?

advertisement | advertise on newsday

The wildest one was in ’68, and I don’t think that will happen again, as divided as the parties have been. My operating theory is that the unforeseen will occur. We don’t know what that will be, but there will be something at both conventions that will surprise in some fashion — the vice presidential nominee, fight over the platform, the behavior of people on the floor or podium. It’s an American ritual and the reason I got into this business, watching John F. Kennedy and Richard Nixon [in 1960] and have been doing it here at NBC every year since 1968.