In a medium pot, add oil and heat at medium heat. Cook eggplants on the skin side down for a couple of minutes. Turn over and add Dashi, Soy Sauce, Sake, Mirin, sugar, and 1 1/2 Tbsp grated ginger. Cover and cook for 15- 20 minutes until tender. Remove from heat and let cool (do not remove the eggplant from the sauce while cooling).