The first thing you’ll notice about “Pieces of April” is how it looks.

Shot on a handheld digital camera in 2002, the image quality is flat and noisy, like an old home movie. But once your eyes adjust, the film — which is streaming on the Criterion Channel this month — begins to work on you.

It takes place on a single Thanksgiving day on the Lower East Side, jumping between parallel stories of a New Jersey family piling into the car to visit their estranged daughter in the city, and the daughter frantically preparing to host them in her Suffolk Street walkup.

It’s both deeply of its time, and shockingly modern, with a cast as diverse as New York City that doesn’t tout its own diversity, and with takes on race and love and identity that feel like they came from a Gen Z filmmaker, and not one from Gen X.

Writer and director Peter Hedges — father of the actor Lucas Hedges — began his career in theater, moving to New York in the 1980s to direct off-off-Broadway plays in a little theater company with Joe Mantello (now a Tony award-winning actor and director), Mary Louise Parker and others.

On the subway one day, he saw a young actress reading a script and struck up a conversation. She told him about how, on her first Thanksgiving in town, her oven broke down, and she had to go door-to-door through the building borrowing kitchens to cook in.

“The minute I heard that, I went ‘That is a great idea,’ and I made notes about that idea for years,” Hedges said in an interview last week. “And then forgot about it.”

Hedges went on to great success beyond theater. He wrote the novel “What’s Eating Gilbert Grape?” and then the movie adaptation. His screenplay for “About a Boy” was nominated for an Academy Award.

Meanwhile, life was happening. After his mother was diagnosed with cancer, Hedges and his siblings poured their energy into her care. Hedges ignored his career. Eventually, she checked in with him.

“‘Peter, what are you making? What are you doing?’” he recounted her saying. He replied that he didn’t want to work, that there was no point in making anything, but she urged him to take on a project.

Digging through his computer, he found an old file of notes called “Pieces of April,” about a young woman cooking a Thanksgiving turkey.

“About four pages into my notes, I said ‘Why is she making the turkey? Why is it important on this Thanksgiving?” Hedges recounted. “And my notes said: Because her mother has cancer.” Hedges gasped aloud, he recalled, and telephoned his mother. “Oh Peter,” she said. “This is one you’re supposed to make.”

The script Hedges eventually wrote was so powerful that actors lined up for parts. In a 2003 interview with WNYC, Katie Holmes, who played the lead, said she was so moved by the script that she read it three times in a row.

Derek Luke, the star of Denzel Washington’s “Antwone Fisher,” took a leading role. Sean Hayes called in from the set of “Will & Grace” to request a part. Patricia Clarkson ended up with an Oscar nomination for her part as April’s mother. The R&B singer Sisqó, most famous for his novelty hit “Thong Song,” asked to be in the cast. (Hedges was not familiar with Sisqó’s oeuvre, he said, “but what a delightful man!”)

Hedges tried and failed to get “Pieces of April” financed multiple times. At one point, he’d lined up $6 million in financing, which was the top of the range for a low-budget indie film at the time. But it wasn’t enough to shoot in New York — at that budget, they’d have to shoot in Canada.

"I was up scouting in Toronto going ‘How are we going to make this feel like New York City?’" Hedges said. “And then we lost our financing, which was a great blessing.”

He eventually made the film for $300,000 for the legendary digital movie collective InDigEnt. He had to shoot it on a camcorder and pay his cast $200 a day plus a promise of future profits. But without a big-budget crew, he got to shoot in New York, filming in a run-down LES tenement, with the actual residents of the building appearing as extras.

“Piece of April” was shot in only 16 days, with the cast and crew filming scenes in the family station wagon as actors actually drove the station wagon from one location to the next. On Holmes’ first day on set, Hedges and his crew were three hours late because the car broke down in a scene outside a Long Island Krispy Kreme.

Hedges had wanted to make the film without a score, but colleagues convinced him otherwise. So he thought of his favorite films with powerful music from a single artist, like “Harold and Maude,” “The Graduate,” or “McCabe & Mrs. Miller,” and decided to go for a moonshot.

He reached out to Stephin Merritt of the Magnetic Fields, whose magnum opus “69 Love Songs” had been released a few years earlier. Merritt obliged by making his entire back catalog available and penning four original songs for the soundtrack.

The movie won multiple awards and made more than 10 times its budget in box office receipts. Hedges said it's the only one of his works he revisits regularly, watching it every year at Thanksgiving.

“Thanksgiving is my favorite holiday, and this may be my favorite project I’ve been a part of. We made the film against all odds in a very scrappy way,” Hedges said. “It’s about all the things I care most about: family; that we can make amends for harms we may have done to each other, we can find a way toward a momentary grace.”

Perhaps the most important member of the movie’s audience never got to see it — Hedges’ mother passed away in 2000.

The pair of little ceramic turkeys that appear in a pivotal scene are something she purchased on one of her last times out in the world. Hedges’ mother knew his movie called for such a knick-knack, so she and his sister went out to thrift stores looking for them.

“I think she would have loved it,” Hedges said. “My eulogy for my mom is ‘Pieces of April.’”