At the age of 61, Fran Drescher has started doing stand-up — and she doesn’t want to do it like a man.

“When I do my half hour,” she told IndieWire, “I want to go deeper into life experience, and find the humor in the darkness and despair. I think there’s a shift in female comics, and the way they tell stories, that include things they’re passionate about — whether it’s sexual orientation or health or relationships. I think as women, we’re starting to develop our own style and not just be like the men. That’s what I aspire to be.”

Drescher’s decades-long resume contains many fascinating roles — writer, actress, sitcom star, diplomat, activist — and now, stand-up comedian, a pursuit that’s technically new to her.

So she’s looking to the modern state of the format, as pioneered by comics like Hannah Gatsby. A woman...