으면서 자라다

grow up doing something

"-(으)면서" (while) plus 자라다 "grow up" — what you did through childhood, and so what shaped you. Every line here is about upbringing: grew up listening to that radio show, grew up eating this, grew up on traditional pie and mash, grew up hearing "stop eating, you'll die like that", grew up listening to rock. It is the standard way to introduce a formative background, and the thing you grew up with is where the emphasis lands, not the growing.