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NEW YORK – In “The Honorable Woman,” an eight-part miniseries airing on SundanceTV, Maggie Gyllenhaal stars as Baroness Nessa Stein, a British Israeli heiress whose life is inextricably bound up in one of humanity’s most enduring conflicts.

As a child, Nessa witnessed the brutal assassination of her father, a Zionist arms dealer, and three decades later she is committed to using her wealth and influence to foster peace and prosperity in the Middle East. The series opens as Nessa announces plans to bring high-speed data cables to the West Bank in a lucrative deal with a Palestinian businessman.

“Terror thrives in poverty, it dies in wealth,” she declares idealistically. But within minutes, the businessman turns up dead under suspicious circumstances and viewers are thrust into a complex mystery that involves secrets buried deep in Nessa’s past.

“The Honorable Woman,” written and directed by British TV auteur Hugo Blick, landed on Gyllenhaal’s doorstep at a time when she was frustrated about being sent the same kind of part over and over again – “sexy single mom” roles that were bad versions of the character that earned her an Oscar nomination in 2009’s “Crazy Heart.”

“I was really looking to play an intelligent, powerful woman who was also all the other things that we women all are,” says the 36-year-old over breakfast at a Brooklyn cafe not far from the home she shares with her husband, actor Peter Sarsgaard, “which is confused and weak and broken and not broken and sexy and not sexy.”

Nessa, a character whose stylish and poised exterior barely disguises a profound emotional vulnerability and a history of intense personal trauma – she sleeps in a high-tech panic room, and with good reason – certainly fit the bill. Still, Gyllenhaal says she hesitated to accept the part.

“My husband and everybody who works with me were all like, ‘What are you talking about? You have to do this, it’s a very unusual and extraordinary piece.’ But I really did try not to do it. I tried really hard. I knew that in order to play her I would have to grow up in some major way as myself and that I would probably be a different person by the end of it than before I began.”

Blick had no such reservations about Gyllenhaal. “I didn’t want a casting that suggested an ... action girl or a Barbie doll,” he said via telephone. “She needed to have a cool exterior of intellectual presence. You have to have this outside of calm and then inside you have to be emotionally in bits. I really needed an actor who could perform all those layers, and Maggie was that.”

In a rarity for a spy thriller, even one with the complexity of a John le Carre novel, “The Honorable Woman” is populated with female characters who are more than mere honey traps. Chief among them are Janet McTeer as a steely MI6 boss who coolly gives orders to her ex (Stephen Rea), and Lubna Azabal as a formidable Palestinian woman who works as a nanny for Nessa’s brother (Andrew Buchan) and tightly wound sister-in-law (Katherine Parkinson).

“I was really intrigued to take the chassis, the vehicle of the genre which is quite masculine, and place women at the center of the story,” says Blick, who also wrote and directed the noir series “The Shadow Line.”

Gyllenhaal, who will be making her Broadway debut this fall opposite Ewan McGregor in a revival of Tom Stoppard’s “The Real Thing,” joins a growing list of movie talent migrating to television for creative fulfillment. “Not only are there not that many interesting independent scripts, there’s no real systems to help get them distributed anymore,” she replies when asked about the challenges facing the independent film business. “If you’re making work so that people will see it and be affected by it, it makes a lot more sense to do it in television.”

But even though Sundance is a comfortable small-screen home for an actress who burst onto the scene in the 2002 festival favorite “Secretary,” the move to television was not without risks. For Gyllenhaal, used to the three-act structure and two-hour arc of feature film, the sheer scope of “The Honorable Woman” was unprecedented. And as the mother of two young daughters, she also had to consider how she’d juggle a lengthy shoot that would take her family to London and Morocco with the more quotidian demands of child rearing.

“About the third day, I remember just crying quietly in my trailer and I tried not to mess up my makeup. I hadn’t ever taken on anything like that,” she recalls.

Executives at SundanceTV, which co-produced the series with the BBC, also a partner on last year’s “Top of the Lake,” had few such qualms.

“When Maggie’s name was suggested, it didn’t even take us a beat to be fully in,” says network President Sarah Barnett.

“She’s such a nuanced performer, and she’s so able to convey such layers within a character, and she has this incredibly physical presence.” Barnett, a Brit, also jokes that Gyllenhaal’s plummy English accent “is more impeccable than mine.”

Critical reaction to the series and in particular to its lead performance has been just as positive.