Who or what is observing

I've heard it taught by various secular teachers that through mindfulness one can uncover the "true authentic self" because we realise that we are not thought but that we are awareness of thought. Please correct me if I'm mistaken but in my understanding this is not in alignment with Buddhist teachings and a misunderstanding of mindfulness. We can discover that there is an awareness of thought, emotion etc but are we this awareness? Wouldn't Buddha say that even awareness is not self? If we are not thought, not awareness, who or what is the observer? Is the observer just more impermanent phenomena?