Peel and cut eggplants into 1 inch by 2 inch strips. Mix sugar and Balsamic vinegar. Set aside. Heat 1/2 olive oil in wok. Add 1/2 eggplants and cook, stirring constantly until lightly browned, about 5 minutes. Remove from pan. Heat remaining 1/2 oil and cook remaining eggplant in same fashion. Add all eggplant back to pan. Add 1/2 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.