Wash eggplant and discard ends. Chop into 2” pieces, place in paper towel lined bowl and salt thoroughly. Allow eggplant to ‘sweat’ and release moisture for about 30 minutes.
In a small pot, combine eggs and tea bag and cover with water. Bring to a boil, and then reduce heat and simmer 10 minutes.
To brown the eggs, remove from pot one at a time with a slotted spoon, crack slightly (I hit them gently with the bottom of a mug), and return to pot for an additional 2-3 minutes of cooking time. Turn off heat, drain and rinse with cold water.
Combine cucumber, tomato, red onion and parsley in a medium bowl. Squeeze lemon juice over it, and season with salt and pepper. Set aside.
Heat ¼ cup oil in a deep frying pan on medium high heat. Fry eggplant slices until golden, and then transfer to paper towel lined plates to drain excess oil. Repeat until all eggplant is fried.
Warm pitas in oven for 3-5 minutes. Slit open the tops.
Peel and slice eggs.
To assemble sandwiches, spread bottoms of pita with a tablespoon of hummus. Add Israeli salad (use a slotted spoon to avoid the liquid), fried eggplant and a few slices of egg. Drizzle with tahini and amba sauce.