Heat 1 tablespoon oil in a skillet over medium heat. Add eggplant; cook until golden brown and soft, but not mushy, 3 to 5 minutes per side.
Mix remaining 2 tablespoons oil, lemongrass, garlic, green onion, basil, red chile, and ginger together in a bowl. Pour over eggplant in the skillet. Cook until green onion wilts, about 3 minutes. Stir in oyster sauce and sugar. Cook until flavors combine, 2 to 3 minutes. Remove from heat.