From the little I know of BT's this is not one.
too small
closed eye
sweet and  fruity taste

I will like to say Celeste but not sure.

That is what I think too, Eden.

Celeste

English Brown Turkey is much larger in Breba crop and main crop.
This one look like Celeste,as other people said.

Thanks to all for their input in identifying the variety.
Celeste it is.

Grant,
IMO your pictured fig is a Southern Brown Turkey.
I purchased that cultivar from EL this past winter, they have it labeled as "English Brown Turkey".
Attached are the pictures of the first two (2) figs harvested. We had torrential rains for the first ripening fig which split open after 4 inches of rain.  We had about 1 inch of rain two days ago for the second fig. The next two are swollen and will be ripe in about 4 days. From my observations in takes 7-8 days from first signs of swelling to ripe. I decided to pick it early to be safe, but I will let the next few get riper and darker in color.

I believe that this cultivar is also known as Hanc Mathies' English Brown Turkey and Miller's Brown Turkey from older discussions and descriptions.

BTW the eyes (ostioles) change to a pink color only after the fig starts to swell and change color... in the last days just before it ripens.

The fig had a mild fig flavor, sweet, rich and had seed crunch, but no added nutty flavor. It was a very good tasting fig, although it wasn't fully ripe. Also the skin was chewy but not thick or tough.

I think Pete is right:Tho it look like Celeste we were all wrong,except Pete.
That fig is Southern Brown Turkey.

In 2010 or 2011 I purchased this fig as well from edible landscaping had 2 or 3 figs last year but sadly i ate a coll de dame blanc first so i don't really recall the flavor. Not very big in size but they are hardy.