Rinse eggplant and cut crosswise into 1-inch thick rounds. Cut rounds into 1-inch-wide strips.
Pour vegetable and sesame oils into a 12-inch nonstick frying pan or a 14-inch wok over medium-high heat. When hot, add eggplant and stir frequently until soft when pierced and lightly browned, about 8 minutes. Transfer eggplant to paper towels to drain.
Add ginger and garlic to pan and stir frequently until fragrant, about 1 minute. Add pork and stir until crumbled and brown, about 5 minutes.
In a bowl, mix soy sauce, sugar, vinegar, chili paste, cornstarch, and 1/4 cup water. Pour into pan and stir until mixture is simmering and thickened, about 1 minute.
Gently stir in tofu, eggplant, and green onions until heated through.