The character meets a girl at a party and she tells him this. I understand it's "Please eat a lot, I'll bring some to you"
But what is the second part of the sentence actually? "let me hear about your recommendations"? why is のよ used?
I think you misread まかせて as きかせて. 「おすすめあんのよ、まかせて」 is straightforwardly 'I've got [some] recommendation[s], just leave this to me'.
あんのよ is the verb ある with the explanatory no. The る has contracted to ん. This way of using explanatory no (without the copula だ) is feminine. あるんだよ or あんだよ would be masculine.