Definition of barbola work from the Webster Dictionary: The decoration of small articles (as of wood or glass) with colored models of flowers, fruit, or other ornamental objects made from a plastic paste.
The craft is mentioned from 1924 til 1956 in Trove. It was all the rage in the 1930-40s for decorating picture frames, mirrors, vases, jewellery and the like. Items were moulded then painted and varnished once dry. Barbola paste was made in England from French clay, and sold in tins. By 1947 an Australian made version was on sale. Could this be the substance (or similar) out of which buttons were being made by a firm in Melbourne (see Mysteries page)? Could it be what Carol’s collection of ceramic-type buttons below are made from?
A similar type of button is found on some c.1950 Beauclaire buttons: