Light a grill. Place the eggplants on the hottest spot and grill, turning as needed, until charred and tender, 12 to 15 minutes. Transfer to a cutting board and let cool.
Once cool enough to handle, peel the eggplants. Place over a sieve or colander to drain while they cool completely.
Once cooled, slice the eggplants into thin ¼-inch slices, carefully removing and discarding any seeds. Line a sheet pan with parchment and grease it with olive oil, then lay the eggplant slices on the pan. Cover the slices with another sheet of greased parchment facedown and place a sheet pan on top. Lightly press to flatten the slices.
Remove the sheet pan and top piece of parchment. Place an upside-down platter over the carpaccio and flip to invert. Remove the sheet pan and parchment.
Season the slices with salt and pepper, and a drizzle of olive oil. Then, drizzle the tahini and date molasses over the slices and top with the remaining ingredients. Serve alongside the pita.