Warm naan and some cucumbers make a nice accompaniment to this dish.
Preheat oven to 425 degrees with racks in top and center. Sprinkle eggplants generously with salt; arrange in a single layer on a wire rack set over a rimmed baking sheet. Let stand 30 minutes.
Meanwhile, in a skillet over medium-high, toast cumin seeds until dark brown and fragrant, about 3 minutes. Finely grind in a spice grinder, or crush with a mortar and pestle. Stir together with 2 teaspoons oil, garlic, ginger, and 1/2 teaspoon salt.
Rinse eggplants; pat dry with paper towels. Brush baking sheet generously with oil. Brush eggplants on both sides with remaining oil; season lightly with salt. Arrange in a single layeron sheet and roast on center rack, flipping once, until tender and golden brown, 40 to 45 minutes. Spread about 1/2 teaspoon garlic-ginger mixture over each slice; roast 5 minutes more. Remove; adjust oven to broil.
Divide yogurt among eggplant slices, spreading over tops. Top each with a tomato slice; season with salt. Broil on top rack until just beginning to brown, 1 to 2 minutes. Stack slices three-high, layering cilantro between each. Serve, garnished with more cilantro.