MAX BROOKS says he hasn’t told this full story before, but it is one that informed his early interest in writing about race.

In 1964, Max’s mom, the Oscar-winning actress Anne Bancroft, presented an Academy Award for Best Actor to Sidney Poitier, for his performance in “Lilies of the Field” — the first black performer ever to win this prize. As was custom, Bancroft gave the winner not only the trophy, but also a side kiss.

“It was traditional back then that if a lady was handing the Academy Award to a man, she [gave] him a peck on the cheek,” Brooks tells The Post’s Comic Riffs. And so Bancroft did, right before Poitier spoke of the “long journey” that preceded his historic victory at that lectern. Moments later, the two future co-stars (1965’s “The Slender Thread”) walked off stage together, beaming and glamorous.

All was well, the late Bancroft once told her son, until public reaction came in.

“The shocking part was, as she got hate mail from around the country, the death threats came from the North, not the South,” Max Brooks tells Comic Riffs. “The South was condescending [in tone], like disciplining a bad child: ‘Don’t you know what you’re doing?’ But the North was much more violent in the letters.

“She didn’t want to talk about it … she tried hard to forget it. But I don’t think she anticipated it at all.”

For Max Brooks, it was a poignant story about race that hit home. Another conversation stuck with him from when he was a young boy.

“I was about 11, and a UCLA grad student in history [working for my parents] told me about the Harlem Hellfighters,” says Max Brooks (whose father, of course, is comic genius Mel Brooks). “He told me about it like a throw-away line: ‘You know there was a unit of black soldiers … who came home from World War I as one of the most decorated units in the the U.S. Army.’

“When you are 11 and you are white and are living in one of the most affluent parts of the world [in Los Angeles], being driven home from private school … that kind of injustice could not be more foreign.”

As Max Brooks grew up, the now-bestselling  author (“World War Z,” “The Zombie Survival Guide”) developed his interest in both warfare and racial injustice. Even as he landed a writing job on “Saturday Night Live,” he had a script he’d written about the unit that enemies respectfully dubbed the “Harlem Hellfighters” — the heroic all-black infantry regiment that faced down not only howitzers in Europe, but also the heat and violence of prejudice back in the States.

“We’ve had the pageantry of sending young men off to wars ever since we first had armies — women and children going to cheer you off and buck you up as you go into battle,” Brooks says. “But the Harlem Hellfighters were denied their parade because, as they were told, ‘Black is not a color of a rainbow.’

“But they were not only sent off to war — they ultimately triumphed in spite of everything the Army and the government did to try to sabotage them. They still came home as heroes who weren’t just conquering racism — their combat record was stellar.”

The 369th regiment was all-black because its soldiers were not allowed to fight alongside their white American counterparts in Europe. And so they went to war alongside the French, and won battles and honor and glory; “Hellfighter” Henry Lincoln Johnson became the first American of any race to receive the French Cross of War.

Fascinated by this undersung chapter in World War I history, Brooks tried to sell his script years ago — to no avail. “When I was pitching my script in the ’90s, I had no [Hollywood] muscle and I was a nobody,” he says.

Plus, “It was a period movie, and a war movie, starring all black guys,” Brooks says — in Hollywood’s view, “the trifecta of ‘no.’ ”

“I really blamed myself initially,” Brooks says. “I thought: I’m not doing a good-enough job telling this story.”

Even as he shelved his script, though, Brooks says he retained a belief in the project, thanks partly to the encouraging words of actor/TV host LeVar Burton, who told Brooks back then: “Of all the stories about the Harlem Hellfighters, yours comes the closest.”

In 2003, Brooks helped usher in the current wave of the undead craze with the bestselling humor book “Zombie Survival Guide,” which he followed up with his 2006 horror novel “World War Z: An Oral History of the Zombie War.” As his books gained fans — as well as Hollywood’s attention — Brooks dusted off the Harlem Hellfighters idea, but with a twist: He’d publish it as a graphic novel.

Brooks decided he would blend history and fiction, to give himself some literary leeway. “The core characters would be fictionalized in a way that I would have more artistlc freedom,” he says, “and not have the risk of insulting the [real men’s] families.”

The author reached out to historians who specialize in the African American experience during World War I. “The difficulty,” he says, “was trying to find primary source materials.” And he deftly created amalgams based on such true-life figures as Lt. James Reese Europe, the then-popular bandleader who helped introduce Europe to the roots of nascent jazz, and Eugene Jaques Bullard, who was a a highly decorated veteran of both World Wars before dying as a Rockfeller Center elevator operator in 1961.

Brooks also teamed with Canaan White, a gifted African American artist who makes the viscous violence of trench warfare come alive, even in scenes of bloody death. “I got lucky,” Brooks says, “in finding one of the best artists [at] working in extraordinary detail. … He’s a visual genius.”

Still, Brooks had concerns about how his graphic novel — which was published last month by Broadway Books — would be received. “I was bracing for the reaction,” he says.

From reviews to colleagues’ feedback, that reaction has been positive. One of Brooks’s cinematic heroes, Spike Lee, blurbed the book with praise. And Sony and Will Smith have optioned the film rights to the story.

“I am constantly surprised by the level of interest — I never would have expected it,” Brooks says. “I am stunned and grateful for the positive response. Because this is a white guy writing a black story, I never would have begrudged any African American who said: ‘What gives him the right to do this?’ ”

As opposed to 15 years ago, though, Brooks believes Hollywood is more receptive to this story now because of the changing social backdrop.

“Look at how the landscape has changed, including changes [electing] the first black president has brought,” Brooks says.

“We’re living in a time with the George Zimmerman [case] and Ted Nugent calling the president a subhuman mongrel — there is a backlash that has energized [recent] movies about race,” Brooks says, noting that the recent success of such films as “12 Years a Slave” and “Lee Daniels’ The Butler” helps break down commercial biases within Hollywood. To executives, he says, box office and Oscars talk.

Unlike with the movie “World War Z,” Brooks plans to be closely involved with “Harlem Hellfighters” as a film. “This is a passion project,” he says. And he hopes the cinematic spotlight can help Americans fully see and appreciate the sacrifices and achievements of the 369th infantry regiment — a unit that he believes helped spark empowerment en route to enfranchisement. And a step in that direction, he says, would be honoring one of World War I’s first American heroes.

Henry Lincoln Johnson, the soldier who received the French cross, was born in Alexandria in 1897, and was buried at nearby Arlington Cemetery 32 years later. A decade ago, he received the Distinguished Service Cross. His descendants are still waiting for him to receive a Medal of Honor.

Brooks understands that there are so many men and women from so many U.S. wars to properly honor. His aim is that the Harlem Hellfighters receive their rightful place in the American memory.