Reduce heat to low, and wipe the pan clean with a towel. Add the sesame oil, garlic, ginger, and scallion, and cook, stirring, until fragrant. Increase the heat to high, and stir in the ground beef. Season with a little salt, and cook until the beef is no longer pink. Stir in the eggplant, then the sake, miso, mirin, and shoyu. Continue to cook for 1-2 minutes, until the eggplant is heated through. Serve hot.