Prep the sauce. In a large mixing bowl, whisk the miso paste with the mirin, soy sauce, chili paste, garlic, ginger and sugar. Set aside.
Prep and marinate eggplant. Wash and dry the eggplant, and then cut it into sticks that are about 3-inches long and ½-inch wide. Add them to the sauce as you work, and once all the eggplant has been cut, mix gently to ensure all of it has been evenly coated. Cover the bowl with plastic wrap and let it marinate for about 30 minutes.
Cook. Coat a large sauté pan with the oil and place it over medium-high heat. Once it's very hot, add the marinated eggplant. It should sizzle immediately -- if it doesn't, wait until the pan is hot enough! Brown the eggplant on all sides. This should take a couple of minutes. Then reduce the heat to medium low, and cook just until the eggplant is soft, about another 6 minutes. Deglaze the pan with the sherry and cook just until most of the liquid is absorbed, about 30 seconds or so.
Serve. Add a few mint leaves to the eggplant and serve over rice.