My daughters are growing up bilingual in Persian and English. Totally fascinating to find the cognates; many are surprisingly close still (daughter/dokhtar, star/setare, cow/gav). It’s fun feeling like I could communicate basic ideas to a proto Indo European speaker based on those really distant cognates.
It gets complicated by the preponderance of French loan words, although they tend to be for newer concepts such as car, elevator, etc.
There do also seem to be some genuine coincidences, such as sock it/saket, both being a somewhat forceful way to tell someone to be quiet.
But yes, Persian people and culture in particular has fascinated me due to the ancient, but not prehistoric, traces of a shared identity with Europeans, in contrast with its neighbors. It’s not something that gets a lot of attention in popular culture