Heat grill to medium-high.
In a small bowl, combine the oil and 1 tablespoon soy sauce. Brush the eggplant and fish with it and season with ¼ teaspoon each salt and pepper.
Oil grill. Grill the eggplant and fish until the eggplant is tender and slightly charred and the fish is opaque throughout, 3 to 5 minutes per side for both.
In a second small bowl, combine the vinegar, ginger, jalapeño, cilantro, and remaining soy sauce. Drizzle over the fish and eggplant before serving.
