I'm wondering about the barbe = head part. Doesn't make sense, but I don't know the etymology here.

On a plain folk level, sans dictionary, I wonder whether the barbe part could have been the tusks of a boar's head that could have been barbequed in Virginia at some point in my beloved state's history and very likely in the 17th century. We do have a positively splendid inn in Charlottesville, Thomas Jefferson's territory, called the Boar's Head Inn.