These "pin" or "nut" trays / dishes are fairly common items and are often referred to by paperweight collectors as "related items" (along with anything else that uses "paperweight techniques" but is not a true paperweight).
Paul's example includes canes that are defintely from the early Vasart (pre-56) years but the item could have been made in the later Vasart period or perhaps in the continuation years under the Strahearn name. Current Scottish makers, for example John Deacons, have also made similar items although more usually in a flatter form.
They are made as a basic paperweight, flattened out to some degree, with added glass which is shaped to form the tray / dish rim. The rims vary in height (or depth to the inner base - if you think of it that way) and some examples have upright rims while in others they slope inwards. The same design would become an ashtray if had shallow rests cut into the rim - but all of the few ashtrays I have seen have been larger than the "pin" or "nut" trays (except for the really flat and large dishes / trays!)
The fracture that glasstrufflehunter commented on is not a fracture. The paperweight core is indeed domed to whatever extent the flattening process gave it, and the visible "crack line" seen in the profile view is just the point where the inner dome meets the side wall and is apparant in all of the ones I have seen. The base grinding is quite typical for Vasart work of both the earlier and later years.
UV checks have shown that some items of this type were made pre-1956 (I have an ahstray from the earlier period). Because the UV reaction of later Vasart and Strathearn items is identical, it is not possible to be sure about when some were made. However, as shown in Frank's links, larger dishes with very low profiles were also made, and I suspect that the majority of those were from the Strathearn years rather than the Vasart ones - but I can't prove that.