Preheat the oven to 425°. In a small saucepan, cover the potato with 2 inches of water and bring to a boil. Cook over moderate heat until just tender, about 20 minutes. Drain and let cool, then peel the potato and slice it 1/4 inch thick. Season the potato slices with salt.
Meanwhile, arrange the eggplant slices on a rimmed baking sheet and brush both sides with olive oil. Season with salt and bake for about 10 minutes, until browned and tender.
In a large bowl, add the cucumber, tomato, jalapeño, garlic, cilantro and parsley. Toss with the lemon juice and 3 tablespoons of olive oil and season with salt and pepper.
Cut off 2 inches from the side of the warm pitas to make openings in the pockets. Gently open the pitas. Spread the hummus on the bottoms and 1 tablespoon of tahini over it. Layer the potato slices, eggplant, egg and cucumber-tomato salad in the pitas, along with some of the salad juices. Top with the pickle slices and serve.