One of the ones I knew about was in Culver City, CA, mentioned in a Orange County Weekly blog post.
The blog post says in part:
Finally, the place to be an Southern California food lover that weekend is at the Helms Bakery complex in Culver City, where the Eat Real Festival will take place Saturday and Sunday. While there will be plenty of food trucks there, the focus of the festival is on food making. There will be masterclasses on preserving, fermenting and pickling; there will be a pig-butchery contest; there will be a community oven and sourdough lessons.This sounds like a one-time community oven, rather than a regularly scheduled repeating event.
In fact, when I look at the Eat Real Festival site, I could not find any mention of a community oven. So, maybe it's there and maybe it isn't.