Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the minced garlic and ginger, and sauté for about 30 seconds until fragrant, being careful not to burn them.
Add the cut eggplant to the skillet. Stir-fry for about 5-7 minutes, or until the eggplant is tender and slightly browned.
In a small bowl, whisk together the soy sauce, rice vinegar, sugar, sesame oil, and red pepper flakes (if using). Pour this sauce over the eggplant in the skillet.
Stir well to coat the eggplant in the sauce. Cook for an additional 2-3 minutes, allowing the sauce to thicken slightly and the eggplant to absorb the flavors.
Remove from heat and garnish with chopped green onions and sesame seeds if desired. Serve hot.