In the Instant Pot, combine the eggplant, tomatoes, water, onion, 2 tbs of the butter, garlic, tomato paste, Italian seasoning, salt, and red pepper flakes. Stir to combine.
Add the pasta, and stir. I know it doesn’t look like there will be enough water to cook the pasta. But #trustUrvashi, because the vegetables will release a lot of water. Secure the lid on the pot. Close the pressure-release valve. Select MANUAL/PRESSURE COOK and set the pot at HIGH pressure for 7 minutes. At the end of the cooking time, allow the pot to sit undisturbed for 10 minutes, then quick-release any remaining pressure.
Meanwhile, in a small skillet, melt the remaining 1 tbsp butter over medium heat. Add the bread crumbs and mix well. Remove from the heat; allow to cool. Mix with the Parmesan cheese and set aside.
Preheat the broiler. Add the mozzarella balls to the pasta, and transfer the pasta to a casserole dish. Sprinkle with the bread crumb mixture and broil for 2 to 3 minutes. Serve.