While perusing menus at NYPL, I often came across an item called box stew in the same category as oyster stews. I now happen to run across mention of a specially-made oyster stew box in the magazine Table Talk, a sort of 1800s combination of a fine living magazine and a home hints column:

Oyster-stew boxes are a china novelty. The decoration, shells, sea weeds, and little marine views. They have fitted covers like bouillon cups.

How delightful! I wonder what the less-fancy ones looked like!