Peel and cut eggplants into 3 cm by 5 cm strips. Mix sugar and Balsamic vinegar. Set aside. Heat half olive oil in wok. Add half eggplants and cook, stirring constantly until lightly browned, about 5 minutes. Remove from pan. Heat remaining half oil and cook remaining eggplant in same fashion. Add all eggplant back to pan. Add half teaspoon red pepper flakes, or more to taste. Cook, stirring, one minute more. Remove from heat. Add vinegar mixture and stir until liquid is absorbed. Add parsely. Serve over hot rice.