I think I know what it is... not sure if I will be able to find the name of the variety but I saw packages of the tiny figs, they are dry and split at the eye , on purpose, to help them dry fast. These are eaten with Tea, they have hay color skin (when dry) and are still very sweet, hence the use at tea serving...
Next time I go to market I'll buy some so I can show you guys.... or just take a picture of it.