Maybe this year I'll find the motivation. Here's a vid showing one of the easiest (looking) methods I've seen:

I love the concept.
This couple from Ireland built a bigger version of the type I slapped together in high school :

https://youtu.be/syADJOEv2ZM
It's a bit of a cheat compared to the work that goes into the ancient design, but you can have a pizza party right away rather than waiting a month.

Aye, that's pretty cool. The guy from my video did another oven at some kind of fair that was a temporary thing. He built a wooden igloo as the form and used only the straw-infused cob. Built it and burned the framework out and was using it the next day and for the next three days of the fair.

It cracked more but it worked for the duration of the event and took only 24 hours to build.

I like the oil drum concept for the size and shape, as well as the chimney aspect. I wondered how the clay oven vented; out of the door, I guess.

Seems like you could combine the concepts and use the oil drum as a form, and use something that would retain the shape under the dirt he used to bury it.

Yes. I've always wanted to do that as well. It's on my patio bucket list, two grills, a couple smoker varieties, and decently large earthen oven.