In a large bowl, whisk together balsamic vinegar and olive oil. Add figs to the bowl and gently toss until they are thoroughly coated.
Place on grill or grill pan flat side down. Grill for 2 to 3 minutes (depending on the heat), until grill marks appear. Turn over using tongs or a spatula and grill for another 2 to 3 minutes on the other side.
Remove to a platter or sheet pan and brush each fig on the cut side with pomegranate molasses (you don’t need much).
Arrange 2 slices of goat cheese and 2 to 3 whole figs (4 to 6 halves, to taste) on each of 6 serving plates, garnish with mint leaves, and serve.
To make Pomegranate Molasses simply reduce 1 cup of Pomegranate juice and 1 table spoon of sugar over a medium heat for 20 - 30 minutes until thick and syrupy - about 2 this of its original volume. Note - It will thicken on standing so don’t worry if it is a little runny.