Thanks for the comments.
There are many figs known as Melanzana, but the fig that you mention can be called the true Melanzana, a big elongated fig, with dark purple/black skin, shaped like an eggplant.
That variety is called here 'Pedringiana', and people here know well this fig, and remember to have eaten so many of them during childhood, but now it's impossible to find a tree, but wrongly now most people call with this name any big fig with dark skin.
At other times people here knew well figs and kept them in great care, protecting them from hordes of hungry children and birds; dried figs were a common food during the cold months, used also to sweeten coffee.
There were figs everywhere and of many varieties, but now this heritage is lost.