There are hundreds of figs out there. Many of them are large. It all depends on how your taste in figs run. Check out the figs4fun site. Jon has generously provided an amazing list of varieties with descriptions there is also a forum board of fig fanatics that can answer your questions.

You could also try the fig forum here. Like was said above there are lots and lots of large figs.

in tenn, trick will be to find one hardy enough for your winters. brown turkey is a good choice. of course if you're willing to bring the figs inside for the winter you can grow anything. fig forum has lots of experts, http://forums.gardenweb.com/forums/fig/

You can grow many varieties in your area that will do well for you. I have about 180 varieties.
Here's some of the varieties I have.

Here is a link that might be useful: trees of joy fig trees.

Celeste is one of the most hardy figs. I think winters in Tennessee could take them to the ground some years, so get the hardiest you can.

celeste, hardy chicago, & brown turkey are amongst the hardiest.

bonsaist is a jedi fig master, achieving amazing results for pa. if you give figs all the tlc he does, you can grow almost any fig. otoh, i'm the bad santa of fig growers; i put them on a south wall, throw a little mulch each year on them, let my lawn sprinkler system supply water, & thats it--if they croak, they croak :-)

If your brown turkey is yielding small figs, then you
probably don't really have brown turkey. BT figs are large.
You probably have some other variety.

Brown turkey and Celeste are the most commonly mislabled fig trees. Many fig trees came from Europe with the immigrants in the past, and their names were lost. People thought if it's brown it's a brown turkey. Down south if it looks like a celeste it's a celeste.
I'm not a big fan of BrownTurkey, but Celeste does well if you get the real thing. Hardy chicago, Dark portuguese, Brooklyn White. Many varieties will do well if they bear early enough before our harsh winters.

Bass

See if you can find the variety call Texas Blue Giant. It was introduced in San Antonio Tx by Fanick Nursery many years ago and is a very large brown turkey type fig.

Here is a link that might be useful: Fanick Nursery