Brush the eggplant slices with the olive oil and season with salt and pepper on both sides. Roast on a baking sheet until golden brown and soft, about 30 minutes.
Put the eggs in a small saucepan and cover with cold water by 1 inch. Bring to a boil over high heat, remove from the heat, cover and let sit for 17 minutes. Drain immediately and cover with cold water and ice. Let sit for 5 minutes. Peel and thinly slice each egg.
Slice 1 inch from the top of a pita and open the pocket. Spread 1/4 cup of the hummus on one side, add a few slices of eggplant, a few spoonfuls of the Israeli Salad, some cabbage, few dashes of the hot sauce, if using, and then the eggs. Wrap in foil or parchment. Repeat with the remaining ingredients.
Toss the tomatoes, cucumber, parsley, lemon juice, olive oil, vinegar and some salt and pepper in a medium bowl.