In a small bowl, whisk together the ingredients until smooth. Taste and adjust if necessary.
Sandwich:
Heat 2 tbs olive oil in a large skillet. Brush the pan all over. Working in batches if necessary, fill the pan with the eggplant. Season the top sides and drizzle with some more oil. After about 5-6 minutes, flip them and season again only. Once both sides are golden brown, remove and assemble the sandwich.
Sauce goes on both sides of the bread. Baby arugula is the bed and then its 2 slices eggplant, tomato, mozzarella and then basil.