Preheat the grill to 425 degrees.
Use 2 tablespoons of the olive oil to brush both sides of each slice of egg plant. Season with salt. Place on the grill and cook, turning once, until both sides are browned, about 5 minutes per side.
Heat 1 tablespoon of the olive oil in a small pan over low heat. Add the garlic and thyme and cook just to flavor the oil, about 3 minutes. Remove from heat. Combine the eggplant, garlic, thyme, and oil from the pan with the chickpeas, lemon juice, and 1/2 teaspoon salt in a food processor fitted with a steel blade. Process until smooth, 3 to 4 minutes. With the machine running, pour the remaining 3 tablespoons oil through the feed tube and continue to process until the oil is incorporated. Serve at room temperature or chilled.
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