I pretty much followed this recepie for the dough, replacing the yogurt with olive oil:

https://www.alphafoodie.com/easy-middle-eastern-bread-dough/

I used this za’atar mix that I picked up at my local middle eastern market. Mixed 1:1 with olive oil.

Overall the dough was incredibly easy to make and the result is way better than the prepackaged za’atar breads from the market, but still not quite as good as the ones they make there.