This tastes just like my local Japanese restaurants' does. I hope my instructions aren't too confusing. Whenever I serve this, I give each person an eggplant half so they can eat the eggplant out of the eggplant shell.
In a small bowl, combine first 7 ingredients. Set aside.
Wash your eggplants. Cut off the top and then cut in half length wise. If necessary, make the eggplant halves short enough to fit into a 12" skillet. Using a knife, make criss cross marks on the eggplant, making sure that the eggplant doesn't break apart. Leave skin on eggplants.
Heat 1 tablespoon oil in 12" skillet.
Heat oil over medium high heat. Lay 2 eggplant halves in pan, followed by 1/4 water. Cover and let cook for 7-10 minutes or until eggplant is lightly browned. Carefully remove eggplant halves from skillet; set aside.
Repeat with 2 other eggplant halves and other tablespoons oil.
Pour sauce mixture into skillet and cook for 2-3 minutes or until thickened.
Pour sauce over the criss-crossed side of eggplant. Sprinkle sesame seeds on top.