Combine water and salt in a large container, whisking to dissolve the salt. Cut eggplants in half lengthwise, then slice into 1/2-inch-thick half moons. Add to the water. Fit a plate on top of the eggplant and place something heavy on it, such as a can, to keep the eggplant submerged. Soak for at least 1 hour and up to 2 hours.
Meanwhile, combine cilantro, parsley, 3 tablespoons oil, lemon zest and juice, garlic, coriander and cumin in a large bowl; set aside.
Drain the eggplant; thoroughly pat dry. Line a baking sheet with paper towels. Heat 3 tablespoons oil in a large cast-iron skillet over medium heat. Add a third of the eggplant; cook, turning once, until dark golden brown and almost charred, 3 to 5 minutes per side. (If you think it's done, give it another minute or two so it's really creamy inside and crisp outside.) Transfer to the prepared baking sheet to drain. Repeat with the remaining oil and eggplant in two more batches.
Gently stir the eggplant into the herb sauce. Let marinate at room temperature for at least 15 minutes and up to 2 hours before serving.
Make Ahead Tip: Let stand at room temperature for up to 2 hours or cover and refrigerate for up to 1 day (bring to room temperature before serving).
1 1/2 vegetable, 4 fat