Combine Sauce: In a small bowl, stir together miso, soy sauce, vinegar, chili flakes, 2 tbsp water and sugar, if using. Whisk until smooth. Set aside.
Stir Fry Eggplant: In a large wok or skillet, heat oil over medium high heat. When the pan is hot, add eggplant and green onion whites. Cook for 8-10 min, stirring often, until eggplant is tender and golden on all sides.
Add ginger and garlic. Cook for another 1 min, stirring often, until fragrant.
Reduce heat to medium, then add sauce. Cook for 1-2 min, stirring constantly, until eggplant absorbs the sauce.
Serve: Transfer to a platter. Drizzle with sesame oil. Sprinkle with remaining green onions and sesame seeds, if desired.