Preheat oven to 425°F.
Cut each eggplant in half lengthwise. Score the inside of the eggplant in a cross-hatch pattern. Brush the cut surface with 1 tablespoon oil and sprinkle with ¼ teaspoon each salt and pepper.
Place the eggplant, cut-side up, on a baking sheet. Roast until soft, about 45 minutes.
Meanwhile, heat the remaining 2 tablespoons oil in a large skillet over medium-high heat. Add onions and cook, stirring often, until golden brown, about 10 minutes. Add garlic, serranos, baharat and the remaining ¼ teaspoon each salt and pepper; cook until fragrant, about 2 minutes.
Mix lime zest and juice in a small bowl.
To serve, spoon the lime mixture over the eggplant. Pile on the onion mixture and dollop with yogurt. Top with tomatoes and parsley.
