How to Make It
Light a grill or preheat the broiler. In a mortar, mash the garlic with the sugar, crushed red pepper and a large pinch each of salt and pepper until a paste forms. Stir in the lime juice and cilantro. Transfer half of the mixture to a medium bowl and stir in the water, fish sauce and scallion to make a dipping sauce.
Brush the eggplants with 1 1/2 tablespoons of the oil and season with salt and pepper. Season the chicken with salt and pepper. Stir the remaining 1 1/2 tablespoons of oil into the remaining garlic-lime mixture and spread it all over the chicken. Grill or broil the chicken and eggplants, turning once, until cooked through, about 5 minutes for the eggplants and 12 minutes for the chicken. Transfer to a platter and serve at once with the dipping sauce.