Drawing power of Divorce
She says: "It was based on this idea of this story I knew, of real people who'd been having this very long-term affair. It functioned like an alternate universe, nobody was being hurt and it was very loving and they were both married and marriages were good.
"It confounded me, but I thought it was probably not unique. And so I wanted to explore the idea of marriage in a real way."
Initially, she had imagined "many other actresses" as Frances, but she became increasingly drawn to the character.
"I like that she was difficult. I like that she isn't even remotely like me. I like that she can be withholding and maybe unfriendly, short and not buoyant. There's a kind of rigidity to her, but there's also a surprising freedom. She's strong, but she's also in a purgatory of her own making."
It was a different portrayal of women in marriage from what Parker had seen before.
She adds: "That's the beauty of television, how long a life you get to live that's not your own. It's challenging, but it should be."
Divorce is not a reflection of her private affairs, though it is tempting to parse it for clues as to the state of her near-two-decade marriage to actor Matthew Broderick, with whom she has a 14-year-old son and seven-year-old twin daughters.
A journalist tries to gently pry, asking if she is afraid that one day she might wake up and find that the love has gone. Parker says: "You keep trying to get me to talk about my own marriage. No, it doesn't. Because it's not where I am. Everything is possible, but do I lie awake in bed and worry about it? Absolutely not."
A key consideration for her in returning to television was the huge time commitment required for a full series. She had appeared in a few episodes of season 4 (2012-2013) of the musical comedy drama Glee.
"I was at first more concerned about what it meant for my family. I know how I work," she says.
This is how she works, says her co-star, Church, 56, in a separate interview: "She's there usually before everybody and she's there till the end."
The actor, who worked with her on the 2008 comedy-drama Smart People, adds: "She's very smart and she could run any multinational corporation if it gave her a little bit of time to gear up on what they do.
"She's just multi-tasking all the time and she knows so much about so many different areas of production."
It helps that she had a head start in show business. She made her Broadway debut at the age of 11 in the revival of the play The Innocents in 1976. Roles followed in films such as musical drama Footloose (1984) and comedy Honeymoon In Vegas (1992).
Sex And The City, of course, turned her into a major star and Carrie's fashionista credentials led to Parker scoring endorsements with the likes of clothing label Gap. She also successfully launched her own perfume, Lovely, in 2005, followed by fashion line Bitten in 2007 and footwear line SJP Collection in 2014.
She has balanced a multi-faceted career with a stable personal life. That her marriage to Broderick, 54, has lasted almost 20 years is no small feat in an industry where relationships do not typically last.
She says: "Marriage is something I want to be part of, but it's not for everybody. My position on marriage is that I chose to do it. It's not without complication, but that's the beauty of it."
•Divorce premieres on HBO (StarHub TV Channel 601) on Monday at 10am, at the same time as the United States, with a same-day encore at 10pm. It is also available on HBO On Demand (StarHub TV Channel 602/ StarHub Go).