It would be like a judicial appointment. The executive would make the appointment. You could change that. For example, if you wanted the parliamentary committee to have more power, maybe the parliamentary committee could appoint the independent body. That's a question of mechanics.
The key thing is that once they are appointed, they are independent, just like a judge. A judge could be appointed by whatever Prime Minister, but the fact is that, hopefully, once the judge is appointed, he or she is independent.