Shiraz / Persian / Wild Figs - How to eat them right? How to extract as much flavor as possible?
Shiraz figs are figs grown in Shiraz, much like Florida oranges are oranges grown in Florida.  You use the Shiraz figs, in this case dried ones, as you would any other fig.

You can either eat the whole fruit, or peel them should you choose (that may be difficult with dried figs, but easier after reconstituting them.)

According to Health Food Made Easy:


  Since it’s sometimes difficult to find fresh figs, dried figs are a
  good option. They can be eaten as is for a sweet treat.
  
  Dried figs can also be soaked to soften them, or cooked by themselves
  or with any other dried fruits. They are good stewed, and are usually
  sweet enough to require little or no sugar.


Soaking overnight will give them plenty of time to re-hydrate and plump up, should you choose to do so.



I have not heard of making homemade fig extract, or fig extract at all&mdash;but if you wish to try it, you would use essentially the same method used to make any homemade extract or liquer.

Cover the figs in vodka (or rum, but that brings the rum flavor), and allow to infuse in cool dark place for several weeks, shaking occassionally.  This will be facilitated if you chop the figs prior to beginning the infusion.

You might also try making fig liquor, adding some sugar syrup to the infusion.  You will find multiple recipes of you google; the linked one is only an example.