Not sure what it is from the picture. Could it be a partially digested juvenile urchin? You might try using "A Practical Guide to the Marine Animals of the Northeast North America" by Pollock. It is a really good key.
I presume both structures on the photo are similar objects, the left one intact and the right one opened up to show the interior. The pearl-like structure reminds me of a fish-eye lens as mentioned above by Jean-Lou Justine. In that case the left structure would be the sclera - the outer part of the the eye. The resemblance to a sea-urchin skeleton is only superficial, it clearly lacks the pentaradial symmetry of a regular echinoid and spine attachments. And a sea urchin does not peel like an onion.