To make the sauce, combine the mirin, cooking sake, miso, sesame paste (or tahini), soy, rice vinegar and water in a bowl. Whisk until well combined and set aside.
Cut the eggplant into round, 1 cm thick slices.
On high heat add the oil to a large saucepan. When the oil is hot, add the eggplant and cook until golden brown on each side.
Add the sauce and continue to cook until the sauce thickens and eggplant becomes soft. The sauce should glaze & coat the eggplant when cooked. If the eggplant is not soft & sauce is too thick, then add little more water. Remove from pan and serve in a bowl.
To serve, finely slice the green end of the shallot and sprinkle on top of the eggplant, along with the sesame seeds.