The key to Sabich is the balance of creaminess (hummus, tahini, yolk) and acidity (pickles, salad, Amba). For a perfect sandwich, each component must be prepared separately and then layered into a warm pita pocket.
You can either pan-fry the eggplant for an authentic flavor (which is classic) or bake it in the oven with olive oil to reduce the fat content.
Hard boil the eggs (for Sabich, they are best cooked so the yolk is still slightly tender, about 6-7 minutes). Peel and slice them.
Prepare the Tahini sauce (if not ready): blend tahini paste, lemon juice, garlic, and ice water until light and runny.
For the salad, combine diced tomato, cucumber, parsley, and lemon juice. Salt to taste.
Salt the sliced eggplant rounds and let them 'sweat' for 15 minutes to remove bitterness. Pat dry with a paper towel.
Heat the oil in a skillet over medium-high heat. Fry the eggplant in batches on both sides until dark golden brown and completely soft (about 3-4 minutes per side).
Place the finished slices on a paper towel and lightly salt them.
Warm the pita bread (in a dry pan or oven). Cut it open at the top to form a pocket.
Spread a generous layer of hummus inside the pocket.
Layering (best in this order): Place 2-3 slices of fried eggplant on the hummus, followed by egg slices and pickled cucumber slices.
Add a spoonful of the salad (without excess liquid) and optional slices of boiled potato and Amba sauce.
Generously drizzle the entire sandwich with Tahini sauce so it soaks through. Serve immediately while the eggplant is warm.