Slice eggplant into 1/2" slices. Lay out slices in one layer on paper towels. Generously salt each side and allow to sit for 20 minutes. (this process is called "gorging" and removes bitter water from the eggplant)
While eggplant is resting, dice cherry tomatoes into quarters and place in a small bowl.
Finely chop basil and add to tomatoes.
Pour 1/8 cup of the olive oil and the Fig Balsamic into the bowl with tomatoes. Add 1 teaspoon sea salt and 1 teaspoon fresh cracked black pepper and toss. Set aside.
Once salted eggplant has rested for 20 minutes, rinse both sides of each piece under warm water to remove the salt. Pat dry.
Using a silicone brush, coat each side of eggplant with olive oil. Place on barbeque over med-low flame. Grill each side for 10 minutes or until browned and tender.
Stack slices of eggplant and pour tomato mixture over the top the eggplant. Serve immediately.