In a blender or food processor, combine the basil, mint, 1/4 cup stock, chopped green onions, garlic and ginger. Pulse until the mixture is minced but not pureed. Set aside.
In a large, nonstick frying pan, heat 1 tablespoon of the olive oil over medium-high heat. Add the eggplant, yellow onion and bell peppers and saute until the vegetables are just tender, about 8 minutes. Transfer to a bowl and cover with a kitchen towel to keep warm.
Add the remaining 1 tablespoon olive oil to the pan and heat over medium-high heat. Add the basil mixture and saute for about 1 minute, stirring constantly. Add the chicken strips and soy sauce and saute until the chicken is almost opaque throughout, about 2 minutes.
Add the remaining 1/2 cup stock and bring to a boil. Return the eggplant mixture to the pan and stir until heated through, about 3 minutes. Transfer to a warmed serving dish and garnish with the sliced green onion. Serve immediately.