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To make the peanut sauce, combine the coconut milk, peanut butter, ginger, garlic, sugar, soy sauce, and lemon juice in a bowl or food processor. Blend until smooth. Transfer to a saucepan and simmer over low heat until slightly thickened, stirring frequently, about 10 minutes. Set aside.
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In a small bowl, combine the coriander, cumin, sugar, salt, and cayenne. Set aside.
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Preheat the broiler or grill. Place the eggplant in a large bowl and drizzle with the oil. Toss to coat. Sprinkle the eggplant with the reserved spice mixture, tossing to coat. Press any remaining spice mixture from the bottom of the bowl into the eggplant so the spices adhere.
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Thread the eggplant onto the skewers and place them under the broiler or on the grill until softened and well browned, 5 to 7 minutes per side.
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Arrange the skewed eggplant on plates lined with the shredded lettuce. Drizzle the skewers with some of the peanut sauce and divide the reserved peanut sauce among 4 four small dipping bowls and place them on the plates with the skewered eggplant. Serve at once.