Bring 1 cup water to a simmer in a skillet or pot that's wide enough to hold the eggplants and has a lid.
Split each eggplant lengthwise with a sharp knife, then score the skin in a cross-hatch pattern 1 inch apart. Sprinkle the flesh side of each eggplant with salt and gently massage it in. Toss the eggplants in the simmering water. Cover and steam until tender and the water runs dry, about 5 minutes.
Use a large spatula to remove the eggplants from the pot. Pat dry with paper towels and brush the eggplant's scored flesh with about 1 cup tandoori paste to cover the surface. Move your broiler rack to the second-highest position, then turn the broiler on high.
Line a baking sheet with parchment paper and place the eggplants on top. Sprinkle a handful of mozzarella evenly over each eggplant. Broil until the cheese has melted, 1 to 2 minutes. Allow the eggplant to cool slightly.
Sprinkle the eggplant with the toasted breadcrumbs. Mix the yogurt with the remaining 1/2 cup tandoori paste and 1/4 cup water in a bowl to make a sauce. Plate the eggplant with a side salad and spoon the sauce over the top.
Although this recipe uses a tandoori paste, this dish would work with whatever paste or sauce you prefer. Feel free to experiment with miso or pesto.