Nothing scratches that particular blend of historical puzzle and airport-thriller pacing like Dan Brown. I'd argue Steve Berry is the absolute closest match. His Cotton Malone series—starting with 'The Templar Legacy'—hits nearly the same notes: a historian or academic protagonist, shadowy historical societies, globe-trotting to famous locations, and a treasure-hunt plot built on real-ish historical riddles.
James Rollins is another solid bet, though he leans way harder into the scientific and ancient mystery side, sometimes verging on sci-fi. Think 'Sandstorm' or 'Map of Bones'. It's like if Brown's conspiracies got injected with a dose of Michael Crichton's techno-thrillers. The pacing is relentless, maybe even faster.
For a slightly different flavor, Raymond Khoury's 'The Last Templar' came out around the same time as 'The Da Vinci Code' and has that same energy, focusing heavily on Templar lore. I remember grabbing it off a shelf because the cover looked familiar and breezing through it in a weekend.