Salt the eggplants by peeling back a strip of skin on the opposite side of the cut side. Allow the eggplants to drain on a rack over a baking pan for about 20 minutes.
Rinse the eggplants and squeeze the moisture from them, then use a paper towel to pat them dry.
Mix together the mirin and soy sauce in a bowl.
Use a large skillet and heat oil on medium heat until it is hot but hasn’t started to smoke yet. Fry your eggplants with the peeled sides facing downwards. Keep cooking until the undersides have browned, which should take about 5 or six minutes.
Turn the eggplants over and brush them with your sauce mixture.
Keep frying the eggplants for 5 minutes, then add in the rest of your sauce mixture and cook for about two minutes. You should cook them until the liquid has been fully absorbed, and the eggplants will need to be turned once or twice in this period.