They said in an earlier chapter that Shinobu inherited the tongue of her family, so I imagine with Taisho's comment about her being a good taste tester she might have a sensitive palate akin to Erina from Shokugeki no Souma, though not as extreme.
Either you do it low and slow, like what's done in this manga, or you pressure cook it. I'm more of a fan of the low and slow way, always end up with nice broth too.
I mean, he isn't wrong about the origins. Burdock root probably was originally eaten in desperation and cuisines that use parts of the animal that would normally be tossed out come from having to use the entire animal.
We tend to forget the humble origins of a lot of foods we eat. And isn't just forgetting historical things like "lobster used to only be eaten by the poor"; beef brisket and pork belly used to be cheap cuts prepared and eaten only by the working class.