Fifteen years ago, Jim Beam master distiller Booker Noe tasked his son, Fred Noe, with promoting and selling Knob Creek, one of Jim Beam’s small-batch brands. Three years later, the elder Noe passed away, leaving the bourbon powerhouse in his son’s hands.

One day, Noe came across a batch of Knob Creek barrels dated 2001—the same year he’d been assigned what he now calls his first major project for…