This device was used to cook waffles over an open fire. This style of cooking waffles came to America with Dutch immigrants to New York, New Jersey, and Pennsylvania in the 17th century. The waffle iron was a cast iron hinged device with a long handle and a locking clasp at the end to hold the handles together. The handles open in a scissor-like manner to accept the waffle batter.
On the exterior of one of the two waffle irons, there is a mark - “Chatham”. There were a number of small foundries located in Chatham, Connecticut but the tool at Smith’s Tavern does not appear to have any additional markings that would indicate the exact manufacturer.
Reference (similar item): https://www.worthpoint.com/worthopedia/antique-cast-iron-fireplace-waffle-iron-b-w-co