Place the eggs in a small saucepan with water. Bring to a boil and immediately turn off the flame. Cover the pot and let sit for nine minutes. Remove the eggs and rinse under cool water. Peel and slice eggs and place in a small container.

Slice the eggplant into half-inch-thick slices. Drizzle with oil and hot sauce. Broil, flipping once, until lightly charred. Wrap in foil.

Pack the components separate from the sandwich and assemble before eating. Slice pita in half. Stuff with egg and eggplant slices, greens, and chickpeas. Add more hot sauce if desired.