NBC’s new series The Hunting Party melds a lot of TV genres into one high-concept hour. A drama about intelligence officers tracking down serial killers who’ve escaped from a secret government prison, it straddles the line between procedural and serialized mystery over the course its 10-episode first season.

“We really connected when we first met over wanting to do a procedural that felt a bit different,” says creator and co-showrunner JJ Bailey, who met fellow showrunner Jake Coburn on a “creative blind date” set up by Universal Television. “We love big serialized mysteries, but we also wanted to do a big week-to-week cases.”

Starring Melissa Roxburgh as an FBI special agent who shares a personal history with many of these criminals, each episode of the first season finds her character track down a different killer — sometimes creeping out the actress in the process. And while the writers have...