Heat the oven to 355°F/180°C with convection, if possible. Line a large rimmed baking sheet with parchment paper.

Cut the eggplants into 1-inch/2½-centimeter cubes and place in a bowl. Drizzle with olive oil, season with kosher salt, and toss to coat. Spread on one half of the prepared baking sheet. Cut the potatoes into ¾-inch/2-centimeter cubes, toss with olive oil and kosher salt, and spread on the other half of the baking sheet. Roast until the potatoes are golden brown and the eggplants are tender, about 35 minutes. Let cool slightly.

Meanwhile, place the eggs in a saucepan and cover with cold water. Bring to a boil over medium-high heat, then remove from the heat, cover, and let stand for 10 minutes. Transfer to an ice bath, peel, and halve.

Quarter the cherry tomatoes. Thinly slice the red onion, cucumbers, and scallions. Toss the vegetables with olive oil and kosher salt in a large bowl or directly on a serving platter.

Top with the roasted eggplant and potatoes, halved eggs, chickpeas, and chopped cilantro. Gently toss or arrange by hand.

To make the tahini sauce, whisk together the tahini, lemon juice, garlic, water, and a pinch of kosher salt until smooth and pourable. Drizzle generously over the salad and serve with warm pita.