Ina Garten's Assistant Once 'Dismissed' a Letter from Jennifer Garner Asking to Be on Ina's Show (Exclusive)

Ina Garten and Jennifer Garner's friendship almost never was.

"I just admire her enormously," Garten, 76, tells PEOPLE for this week's cover story. Garner also often raves about the celebrity cook and her recipes on her own Instagram series, Pretend Cooking Show (which takes inspiration from Barefoot Contessa). But a simple mishap almost kept them from connecting.

Garten's Food Network shows — Barefoot Contessa and her latest, Be My Guest — always feature her cooking for friends (and husband Jeffrey) at home.

"People who didn’t understand that the guests on my show were my friends in real life often wrote to see if they could cook with me," Ina recalls in her new memoir, Be Ready When the Luck Happens. "[My assistant] Barbara handled my correspondence and always sent polite letters explaining how the show worked. One day, she’d offhandedly dismissed a letter from Jennifer Garner because she apparently didn’t realize who she was."

Luckily, Ina "had an instinct about her."

"She seemed smart, funny and so grounded, very un-Hollywood," writes Ina. "I thought she was someone I could have fun with. I reached out to her when we were shooting an episode in Los Angeles, made a date to cook together, and, as we both suspected, felt an instant connection. We’ve been friends ever since."

Ina remembers their first meeting being around the time of Garner's 40th birthday. (She is 52 now.)

"She very sweetly invited me to her birthday party, which was amazing," Ina tells PEOPLE. "And I loved it because it was 40 women that were invited in their sweat clothes and they were instructed not to have their hair done or anything, hair in a ponytail, sweat, clothes and sneakers. And they were wonderful, wonderful women and it was a very good time."

More recently, Garner appeared on Be My Guest in April. The two made cornbread and pizza crackers in Ina's East Hampton, N.Y. kitchen. That same day, they filmed an episode of Pretend Cooking Show.

"Making a Pretend Cooking Show with the Contessa who inspired it was 🤯 meta for my brain. I always love meeting up with you," said Garner.

Adds Ina: "She is grounded and principled and smart and incredible parent and great cook. She's just extraordinary."

Be Ready When the Luck Happens comes out Oct. 1 from Crown Publishing Group and is available for preorder now, wherever books are sold.