Jujubes. This is an Indian Jujube, which would not grow here, in my zone (9a), but it grows very well in North Fort Myers, at ECHO Farm.
You can eat either the green ones, which were slightly crunchy and more balanced in its acid/sweet, or the yellow and leathery one, which tasted exactly like a slightly spoilt dried apple. I don't know what this varietal is, but I wasn't terribly impressed with the flavor. I was eating fruit that I'd picked up from the ground around the tree, so maybe I need to try it again. Judging by the smell around the tree, you could make some pretty potent wine from these.
The Jujube tree at ECHO is huge, much larger than the Chinese ones I've seen advertised. This one was at least forty feet, and dominated a courtyard with its gnarled and twisted limbs that reminded me of a mulberry.