The Beak is more like our fingernails that a tooth. It continues to grow from the root to the end. Parrots activity use their Beaks to investigate and as you noted to tear things-up.
In their natural setting, their Beaks would be busy all the time, access food sources, like carving in to a branch or seed packet, even after a larva. This supports your need to provide them things to tear apart. Left to their own choices, they will likely find something that you do not want to be chewed.
Lossing /flaking and entire outer layer is something that I have not seen or heard of, but Patagonians tend to find a join in cutting away limestone. It is more likely that your Parrot dislodged a thin lay and popped it off. With time, that layer will fill back in as the Beak continues to grow.
Enjoy!