Well, I have a hypothesis that they may have been used for molybdomancy – divination with molten lead/metal. Pouring molten metal into cold water and then divining something from the shape that forms still exists today and is quite an ancient form of divination. This was historically known in Cornwall, with the molten lead being poured through the hole in a door key handle into water. The hole in the ancient spoons made me think of a small amount of molten metal – tin, lead or perhaps gold – being poured through the hole and the splashes on the other spoon somehow signifying something according to the quarter markings. The doubt in my mind is that perhaps the spoon used for the melting part would have become far too hot to hold, but tongs of some sort may have been used.
Molybdomancy is still a traditional practice in Germany, part of central Europe and Finland at Christmas and New Year and it is also used in Turkey.
As I said, just a hypothesis – after all, we can’t be sure that they were actually used for divination in the first place.