I found that Batmanglij exhaustively covered the meals we had as a first-generation immigrant family (my brother and I were the second generation). There were some notable differences in her recipes - she adds rosewater to many dishes whereas my family did not. I assume that's partly due to regional differences, and partly just family tradition, akin to how different American families might cook something like lasagna. She also sometimes recommends different meats, but this is something I'd already come to expect when meals were cooked by different family members.
I also really appreciated her ingredient glossary because some of the ingredients that I remember by Farsi name aren't really available in the west, or have more generic names. For example, we always used chives in place of 'tareh', which it turns out is actually a Persian leek. But it's nothing like the leeks you find in western supermarkets.
Persiana was a little disappointing, as I imagine most of the more Anglophone cookbooks would be if you're looking for Iranian home style cooking instead of elevated, somewhat generic Middle Eastern cuisine. But to be fair, it does have some delicious recipes nonetheless.
The author's comments about the lack of southern cuisine are interesting. I suspect part of that is simply due to the fact that the north of Iran is far more populated, but I'd be interested in seeing more recipes because of the different cultural and culinary influences in the south.
Also, just like Italian recipes, it is sufficient to get the onion to a translucent state. 8-10 minutes will do. OP and family's arduous caramelizing process is a bit over the top.
Very interesting, btw, of OP mentioning her family insisting on her not learning cooking. My mother had the same precise experience. Of course she chose to learn anyway, which is a good thing as she is an exceptional cook.
I disagree with you on the onions, though. It's one thing to get them translucent, but that's barely caramelized, if at all. Only once they're nice and brown do you get that subtle sweetness.