Forget Twitter. This Musk Is Into ‘Toe Curling Yumminess.’

First Look Media is the biggest Passionflix investor, although that company’s chief executive, Michael Bloom, declined to disclose the size of its stake. (Ms. Musk remains Passionflix’s majority owner.) First Look, founded by Pierre Omidyar, the eBay billionaire, is made up of several unconnected entities. There is a nonprofit arm focused on investigative journalism and documentary filmmaking. An entertainment studio, Topic, specializes in prestige films like “Spencer,” “Spotlight” and “The Mauritanian.” A relatively new division houses niche streaming services, including Topic.com, which focuses on crime, and Passionflix.

“We fully understand that we’re walking at the feet of elephants,” Mr. Bloom said, referring to all-audience streaming services like HBO Max and Netflix. “But we’re not trying to be them. There is an opportunity for specialty services like Passionflix to superserve a particular audience in a way that the big, mainstream retail guys don’t do.”

Romantic escapism used to be a television staple. It was powered by the miniseries (“The Thorn Birds,” “Hollywood Wives”) in the 1980s and the movie-of-the-week in the 1990s (all of those moaning Danielle Steel adaptations). But networks largely abandoned those formats in the 2000s. Cost was one reason; networks also began to favor repeatable crime procedurals and reality shows, including the romance-driven “Bachelor” franchise.

Over the last decade, only a smattering of romance novel adaptations have made it to television. Even fewer (“Outlander” on Starz, “Bridgerton” on Netflix) have been hits.

Passionflix was not conceived as a cynical way to cash in on the streaming boom, Ms. Musk said. Rather, she and two friends, Jina Panebianco and Joany Kane, wanted to make spicy romance television and could not find buyers in Hollywood.

“So we had to create a distribution solution,” Ms. Musk said.

Ms. Musk, named after Puccini’s opera, studied film at the University of British Columbia in Vancouver. After graduating in 1997, she worked for Alliance, a Canadian production company, before moving to Los Angeles, where she directed, wrote and produced a movie, “Puzzled” (2001), with backing from Elon. She ultimately began producing and directing TV movies for Hallmark, Lifetime and ION Television.

But she was frustrated. “I kept getting into conflicts with network executives, who were not interested in stories about empowered women embracing their sexuality.”