Most everyone remembers the iconic photo of Yitzhak Rabin and Yasser Arafat shaking hands in the White House Rose Garden in 1993, with Bill Clinton holding the historic enemies in a solicitous almost-embrace after the signing of the Oslo Accords.

What hardly anyone knows, however, is that the real negotiations for the first-ever agreement between Israel and the Palestine Liberation Organization had secretly been happening for more than a year in and around Norway, of all places, between people unknown to history and without meddling from the major — apparently clueless — big powers.

If that improbable fact fascinates you, so probably will “Oslo” — J.T. Rogers’ ambitious three-hour, fact-based fiction that director Bartlett Sher and his creative team (“South Pacific,” “The King and I”) have lovingly, painstakingly staged at Lincoln Center Theater’s Off-Broadway Newhouse.

The political making of sausage is legendarily not a pretty sight. It is also pretty talky. Still, Rogers, Sher and their generous, marvelous cast do much to lighten the agonizing back-and-forth of the rogue operation with convivial unlikely scenes of eating, joking and drinking among fierce adversaries.

There is a plot-driven cinematic quality, much as there was to Rogers’ “Blood and Gifts.” In that 2011 drama, also directed by Sher, Rogers explored America’s covert involvement in the Soviet Union’s war with Afghanistan in a play that may have worked better as an action-packed espionage movie.

“Oslo,” despite its even-more complicated backstory, feels naturally theatrical. The spare, elegant rotunda set (by Michael Yeargan) transforms from city to city, room to room, by having actors roll in tasteful tables and chairs. A formal double door separates the serious talks from the casual mealtimes.

As we soon learn, this “back-channel” scheme is the brainstorm of a Danish diplomatic couple— Jefferson Mays (touchingly winsome) and Jennifer Ehle (gracefully no-nonsense). He is a sociologist with a theory about face-to-face, intimate negotiations without “road maps.” His wife, in real life now the Norwegian ambassador to the United Kingdom, was his student.

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Thus, while official, big-power peace talks are getting nowhere, these unknown neutral parties have persuaded the PLO finance minister (Anthony Azizi, formidable and compelling) and a Marxist PLO official (Dariush Kashani, furious and funny) to participate. At the beginning, Israel sends two small-time academics (Daniel Jenkins and Daniel Oreskes, who doubles as former Israeli President Shimon Peres). As things progress, Peres sends a high-stakes player (Michael Aronov, insolent and full of life).

The meticulous work behind the short-lived accord leaves us even more hopeless about the world, but a bit more upbeat about the storytelling possibilities of the theater.