PERHAPS YOU’VE HEARD the term “grass to glass” bandied about at the cocktail bar. It has nothing to do with marijuana legalization but is, rather, a new phrase applied to an old concept: agricole rum.

Most rum is distilled from a base of molasses, a byproduct of sugar refining. This type typically delivers rich vanilla and toffee notes. The style known as rhum agricole (agricultural rum), native to the French West Indies, is made from the juice of freshly pressed sugarcane. It conveys the distilled essence of sugarcane, actually...