These funny little glasses are typically French.
They are designed to hold a single Prune (or Greengage) that has been soaked in Eau de Vie.
Traditionally at the end of a meal one would have a Prune, and a very small amount of the liquid, to accompany your coffee.
Whilst washing the glasses recently (I've been delving into the very back of cupboards), I noticed that a couple of them would contain very much less liquid than the others. One was so solid with glass that it was almost impossible to put any liquid into it at all; the Prune itself just sat on the top of a glass with no bowl, no doubt those particular glasses being reserved for that notorious 'Uncle Maurice' who might otherwise end up under the table.
Recipe: Soak semi-dried Prunes in Green Tea over night. Drain the Prunes, and cover with Eau de Vie. Leave for at least a month. At a push, one could use Gin or Vodka.