Fichi Caramellati. Fits, sugar, water, lemon peel & rum. My favorite part of this recipe is slipping the lemon peel into the figs. See https://food52.com/recipes/1014-fichi-caramellati-caramelized-figs
Lucky you, our fig tree has been non-productive for years.... I love this recipe and hope you will try it.
FWIW I tweak the original by starting the caramel first, with just sugar and water in the shallow braiser and I try to take the sugar all the way to just past burnt because I love a bitter caramel. The flavor really complements the sweetness of the figs and the bitterness of the peel.