• Cut the eggplant into ½-inch-thick half-moons.

Line a work surface with a double layer of paper towels; sprinkle the top towel with salt. Arrange the eggplant on the towels in an even layer; sprinkle with more salt. Let stand for at least 5 minutes to draw out excess moisture. While the eggplant rests, cook the onions.

• Peel and thinly slice the onion.
• Finely chop the garlic.

In a pan over medium-high heat, warm 2 tablespoons oil. Add the onions and half the garlic. Season with salt and cook, stirring occasionally, until the onions are caramelized, 10 to 15 minutes. Transfer to a plate. While they cook, prepare the sauces.

• Cut the cucumber into ¼-inch-thick half-moons.
• Zest and juice the lemon, keeping the zest and juice separate.
• Coarsely chop the mint leaves.

In a mixing bowl, combine the yogurt, cucumber, lemon zest, half the lemon juice, half the mint, and the reserved garlic. Season with salt.
In a small bowl, combine the tahini with the remaining lemon juice and 2 tablespoons water. Season to taste with salt.

• Coarsely chop the cilantro.

In the same pan used for the onions, warm 2 tablespoons oil over medium-high heat. Working in batches if necessary, cook the eggplant, stirring a few times, until well browned and tender, 3 to 4 minutes per side. Stir in the onion slices, cilantro, sumac, remaining mint, and 2 tablespoons water. Cook until warmed through, 2 to 3 minutes.

If you have a gas stove, on the stovetop over the flame, warm the pita breads, about 30 seconds per side. Alternatively, toast them in a toaster.

Transfer the eggplant and onions to individual plates. Garnish with the pine nuts. Serve with the tahini sauce, tzatziki, and pita.