Heat olive oil in a heavy bottomed pan over medium high heat. Add eggplant and cook for about 10 minutes, until eggplant softens. Add additional olive oil if eggplants start to burn. Stir in cabbage, turmeric, paprika, and salt. Cook for an additional 10 minutes, stirring frequently, until cabbage wilts. Adjust salt to taste.
Meanwhile, prepare sauce. Using an immersion blender or small food processor, blend tahini, garlic, water, and lemon juice.
To serve, stuff pitas with eggplant and cabbage, cucumbers, mint, and top with tahini sauce.