My neighbor got this from a local nursery about 6-7 years ago, but can't recall what it is.  I'm sure it is one of the more common varieties.  We live in the Seattle area, and temperatures this year have been cool (low 60's during the day), and somewhat rainy.  This is in a location that gets partial sun most of the day. 

The tree/bush is already loaded with figs, but none ripe enough to cut open and photograph right now.  Here are the photos I can provide:

Just a wild guess, Flanders?

English Brown Turkey,and those are Breba fruits.
They will ripe for sure and I am sure you will like them.
If I was you I will break off the main crop that will grow from now on ,on the new growth.
They will be too late to ripe and will make your Breba ripe slower.
The tree will waste energy growing those Main crop,that will come next.