Sadly to say even with my limited experience identifying figs I think it is Brown Turkey by the leaf.  I drive by this tree every day on my way to work.  I stopped on the way home from work today and the owner was packing his car for the July 4th holiday.  I stopped and he glady took me back to his unknown fig tree.  Offered any cuttings I'd like and to come back when the figs are ripe.  He doesn't eat figs but his neighbor comes by and picks the figs which he says are made into jam which he really loves.  The tree is about 15 feet tall.  Owner said it was there when he bought the house and former owner was a landscape contractor.

Nice find. Wasn't there a whole thread about how some figs are accused of being a BT? Also there seems to be multiple strains of brown turkey floating around. Maybe this is one of the better ones. There was a fig tree in Houston that had leaves like that, but the fruit was golden on the outside and inside. I still don't know what it was to this day. 

Would not a real brown turkey have red eyes when the figs are that big?

I live in the woodlands and everybody has fig trees. Most are brown turkey, celeste and Texas Everbearing in the neighborhoods around here as most were built in the eighties till now. I find great unknown varieties in Older neighborhoods with large ethnic populations in houston and other cities. This is where you are going to find unique cultivars not purchased in retail nurseries.I'm Going to Bryan this weekend to visit family and will visit the downtown neighborhoods to search for fig trees. I have scored quite few unique varieties in areas most people would be too afraid to drive through.

Hmmm now that you mention it Houston did have a lot of fig trees.

I kid u not, in my neighborhood
about 1 out of 15 houses on any given st. Has a fig tree. I've done lots of hunting!

I miss Houston. I grew up in Third Ward and moved to the SW side in Alief. There were many figs all about also. Sometimes I never noticed until I looked up to see branches hanging over the fences. If and whenever I go back home for a visit I will take cuttings. 

Steve, ... You never know until you try the figs. Lots of figs have similar leaves. Good Luck.

Justin, ... In several neighborhoods in The Bronx, NYC there are fig trees in 1 out of 4 yards. On one block where you can see into all the yards there are 7 out of 14 Yards.

The Houston area used to be a major commercial fig growing area. There was about 17,000 acres of fig orchards extending from the San Leon area, north between Friendswood and Baytown, up to points northward. There were 17 fig processing plants in the area. They used lye to remove the skin from the figs , and it is claimed the run off from the two canneries in Friendswood was responsible for turning Clear Creek not so "clear" anymore.

The orchards were started by two Quakers (friends) who bought the deed to the land from a banker named League. I once heard the orchards were filled with Magnolia figs, but I don't remember the source.

so do these place still exist to some extent? I never knew that about my own city.

I think the Friendswood Development Company took care of most of them.  I hear stories of a time in the south when there was at least one fig tree in just about every yard.  Since then, most home owners have probably removed theirs.  Driving through the neighborhoods, you should be able to find at least a handful of trees.  Most of the ones I have seen are Celeste, Brown Turkey (in reality they are probably Magnolia), and Alma.

I'm definitely going back when the figs are ripe to get more photos and to taste of course.  Even if it is a BT it would be my first unknown to ID, I'd be a very happy camper with my first ID.  Have to say the owner was very nice considering he was probably on a timeline to get that car packed.