In 2019, veteran TV writer and producer Phil Rosenthal realized he had to move forward without one half of what he thought was “the best part” of his show — but more devastating than that problem was the personal heartbreak that came with it.

In between Seasons 2 and 3 of “Somebody Feed Phil,” Rosenthal’s Netflix food and travel show, his mother, Helen, died from Als. For the first two seasons, Rosenthal would dial Helen and his father, Max, on Skype to regale them with stories about each day’s adventure. The heart and humor of their responses was a large part of what kept viewers watching.

“They were the part that connected the audience to a family,” he says. “I know the audience loves them, because they write to me and tell me. Whenever I post a picture with them, I get the biggest response. I feel like I owe everything that...