Fried Eggplant, Tomato, and Cucumber Salad

Purée cilantro, parsley, garlic, half of chiles, and 1/4 cup olive oil in a blender or food processor until very smooth; season herb oil with salt and set aside. Whisk yogurt, lemon juice, and remaining 1/4 cup olive oil in a small bowl; season with salt and set yogurt sauce aside. Place eggplants in a colander set in the sink; season with 3/4 teaspoon salt. Let sit 30 minutes to drain, then pat dry. Fit a medium pot with thermometer; pour in vegetable oil to measure 2". Heat over medium-high heat until thermometer registers 375 °. Working in batches and returning oil to 375 ° between batches, fry eggplants, turning often, until golden brown and tender, about 5 minutes. Using a slotted spoon, transfer eggplants to paper towels to drain; season with salt. Let cool. Combine eggplants in a large bowl with tomatoes, cucumbers, and remaining chiles; drizzle with some reserved herb oil and toss to combine. Season salad with salt. Spoon reserved yogurt sauce onto a platter, top with salad, and drizzle with more herb oil. Do ahead: Herb oil and yogurt sauce can be made 1 day ahead. Cover and chill separately.