Preheat the oven to 450 degrees F. Arrange the eggplant in a single layer on a rimmed baking sheet. Brush both sides with 4 tablespoons of olive oil.
In a small bowl, combine the paprika, cumin, cayenne pepper, and ½ teaspoon of salt. Sprinkle over the eggplant. Scatter chickpeas around the eggplant slices.
Bake the eggplant and chickpeas for about 25 to 30 minutes, until browned and tender, flipping halfway through.
In a medium bowl, combine the yogurt with the garlic. Season with salt. Smooth the yogurt on one side of a serving platter.
Arrange the warm eggplant and tomato slices on the platter. Top with the chickpeas. Whisk together 1 tablespoon of oil and the vinegar, and drizzle over the salad. Garnish with the pomegranate, cilantro, and flaky sea salt, and serve.