IT ONLY TAKES a wine or two to make a region famous. Take, for example, Burgundy. To many oenophiles, the entire region might as well be labeled "D.R.C." Those are the initials of Domaine de la Romanée-Conti, arguably the most iconic if not the most expensive wine in this tiny corner of central France.

But there is much more to Burgundy than this famous domaine—in fact, there are far more basic Bourgognes (as Burgundies are called in French) than there are grand crus. And when a bottle of the 2010 Domaine de la...