Since 1945, Syrian company Pearl Soap has been using traditional centuries-old methods of making "Aleppo soap" from olive oil and laurel oil. Here's how they do it (I love the contraption they use to cut the soap):
After cutting, the soap is stacked and aged:
The cubes of soap are then stacked in staggered cylinders to allow maximum air exposure. Once they have dried sufficiently, they are put into a special subterranean chamber to be aged for one year.
You can't buy Pearl's soap directly from their website and I couldn't find it anywhere else, but Aleppo soap from other makers is widely available on Amazon and Etsy. (via huit denim)