So at what point did the Central European baba become “baba au rhum?” It clearly had to be during or after the Colonial Era, since there’s no rum without sugar, and the West Indian sugar trade didn’t get going in earnest until about the middle of the 1500’s. But even so it was about another hundred years before the New World’s first rum distillery opened on Staten Island in 1664. So we know it happened sometime after that.
In theory it’s possible that French bakers were making baba au rhum as early as the late 17th Century. However the term “baba” doesn’t officially appear in writing in French until the 18th Century, in 1767. That’s the time when the popularity of babas spread around France and, presumably, when French pâtissiers began adding rum to them. Exactly who was the first to introduce “baba” to “au rhum” remains a mystery, but what a spectacular inspiration it was, because “baba au rhum” has been staple of the pastry department ever since.