Amelie Mancini, a French-born artist living in Greenpoint, had never encountered a baseball card until several years ago, when her boyfriend arrived at her place bearing five or six large boxes of cards that he had brought from home. The two of them—a freshly minted Mets fan and lifelong Yankees fan, respectively—pored over their contents in search of 1986 Mets.

Like many baseball fans, Mancini vividly recalls her first encounter with baseball cards. Unlike most fans, though,...