Sainte-Maure de Touraine

Historically, this practice was used to prevent unwanted microbial life from infesting the cheese on the outside, but it also acts to soften the sharp, tart edge of the caproic and caprylic fatty acids, maybe change it to a more subtly mushroomy flavor.

Or at least this is how it's described for the classic examples, which include French staples like Valençay and Sainte-Maure de Touraine.

There's also an American craft cheese called Humboldt Fog, and I think that was the inspiration of this cheesemonger.

It features both an exterior ash coating and line of ash running through the center of the cheese.