Late-afternoon shadows were overtaking the quiet alley off Polk Street when James Hensel glanced up from the battered cushion that would be that night’s bed and grinned. Striding up the street was his salvation for the next 10 minutes, complete with a crossword puzzle, new socks and something to eat.

It was the Pizza Lady.

“Hey, how about a slice?” the Pizza Lady asked. Hensel, 58, didn’t have to answer. He’s been living in Fern Alley for more than 10 years, and for the past 2½ this woman has been bringing him and every other homeless person on the block a free slice in the afternoon. He took a chicken-pesto piece.

“You’re a good soul, you know that?” Hensel told her.

The Pizza Lady’s real name is Andrea Carla Michaels, and at 58 she has made it one of her life’s missions to hand out pizza to the homeless folks in her Lower Polk neighborhood.

Sometimes she also brings clean socks. Or tampons. Almost all of it is donated from others who know she is the lady who hands out free stuff around Polk Street.

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For some, like Hensel, she’ll toss in a crossword puzzle. It’s another one of her things — in addition to being the Pizza Lady, she composes crossword puzzles for the New York Times.

“I don’t read much out here, but I do like these puzzles,” Hensel said, pulling out a pencil and peering at the latest puzzle she had handed him.

“You know,” he said, “I went to college, used to own a business. I like words. And puzzles like this, they’re challenging.”

Hensel admitted never having finished one of Michaels’ crosswords. “I do the best I can,” he said. Good enough, the Pizza Lady said.

There’s a lot more to Michaels, but most of the street people don’t know that.

“The people I deal with out here never ask what I do or did — it’s humbling,” she said, heading up the alley to a woman folded against a wall, head bowed. “We all take each other as we are out here, just human to human.”

In her non-pizza life, Michaels owns ACME Naming, a company that coins monikers for businesses such as the former Vanguard Airlines. Before that, in the 1980s and ’90s, she was a standup comedian who hit the circuit with the likes of Robin Williams and Will Durst and wrote for television shows, including “Designing Women.”

A Harvard psychology graduate at 20, she was also a quasi-regular on television game shows, famously winning $68,000 on “Wheel of Fortune” in 1991 by guessing “cabbage” with only the “g” and “e” as clues. “That, sadly, was the highlight of my life,” she quipped.

The pizza crusade started on Christmas Eve 2015 when she stopped by Nob Hill Pizza and Shawerma on California Street near Polk, saw a worker tossing an unsold pizza into an empty compost bin, and asked whether she could take it out to feed street people instead. It was still clean, so he heated it up and she passed it out. From then on, Michaels made handing out unsold pizzas from the shop a daily ritual — seven days a week, excepting occasional days out of town, at about 20 slices each time.

Michaels, ever the professional brand-creator, tried to come up with a name in the beginning for what she does. Food First was in the mix, she said, “but everyone just called me the Pizza Lady, so it stuck.”

“These are my neighbors. How could I not do this?” she said one recent afternoon as she made her pizza rounds. “I try not to use the word ‘homeless.’ I tend to see people as haves and have-nots, and these neighbors of mine just happen to be have-nots.

“I think food is the first thing you need in life, and these neighbors don’t have enough of it. If you eat, you can think. And if you can think, you can move forward in your life and try to get the help you need.”

Over the past two-plus years, she’s handed out about 18,000 slices of pizza. Nob Hill Pizza and Shawerma co-owner Yazid Belayadi, 49, said he couldn’t be more pleased about that.

“I didn’t know people like her existed,” said Belayadi, who gives her all those leftover pies for free. “I don’t know why she does it. She just loves it.”

There’s a religious hands-across-the-divide root to what Michaels and Belayadi do, but neither makes much of it. Michaels is Jewish, and Belayadi — a naturalized U.S. citizen who emigrated from Algeria — and his wife, Najet Sehili, are Muslim.

For Michaels, the pizza gig echoes the Jewish tenet of tikkun olam, which urges people to help “repair the world.” For the pizza shop owners, there’s a similar religious belief.

“You cannot push back anyone who asks for something they need, especially food,” Belayadi said. “You are obligated. And, God willing — whatever you do, you get it back. It’s in the Quran.”

Michaels wound up in San Francisco in 1984 largely because of Durst, who saw her act in Boston and told her rightly that she’d be an even bigger hit here, where things are quirkier. Now, all these years later, the famously irreverent comedian also appreciates the hazily theological aspect of his friend’s endeavor.

“What she’s doing with the pizza is the actual religion, the actual spirit, of things when you talk about Christ, Muhammad, Buddha,” Durst said. “She is kind of doing the new spirituality. It’s cool.”

That kind of talk rarely comes up with the people Michaels feeds every day. “I keep it light.” she said.

On a couple of recent afternoons, she dished a slice to a man who hoards so many clothes and knickknacks that his two shopping carts overflow. Another of her regulars lay beside a giant pile of full plastic trash bags that he sleeps under every night. One woman sat morosely and waved away the pizza, but then as she took the dozen tampons Michaels gave her, a tear slid down one cheek. “Thank you,” she mumbled.

Sometimes Michaels includes a few day’s-end bagels from Star Bagel on Polk Street on her pizza run. Star Bagel’s owner, Lap Ley, escaped despotic poverty in Cambodia in the 1970s and takes giving away his food as seriously as Michaels does.

“I grew up with the Killing Fields,” he said when Michaels stopped in for a dozen of his leftovers. “My sister died by starving, and when you watch people starve to death you don’t believe in throwing away food.”

He pointed to Michaels. “A lot of people say they’ll do something like what she does every day, and they don’t,” he said. “She does. She is beautiful inside and out.”

Just before she ran out of pizza one afternoon, Michaels found a bag of shoes someone had discarded. They were in decent shape. Into her load of giveaways they went.

“Hey, I really needed this!” marveled Dean “Shaggy” Schumacher, 37, who was sitting on the sidewalk on Frank Norris Street when Michaels showed up and her bag of shoes contained his size, 9. Out went his tattered old shoes, and on went nearly new-looking black sneakers.

“The Pizza Lady really respects people,” Schumacher said. “There’s a peanut butter and jelly guy who comes out here sometimes, but she’s the main one who treats us like this.” He patted his new shoes admiringly. “Yup, she actually cares.”

Michaels waited until she got around the corner, then gave herself a hug.

“I’m very happy right now,” she said, beaming. “Just ... so happy.”

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com Twitter: @KevinChron