Preheat the oven to 450.
Add the eggplant to a cookie sheet and drizzle with the olive oil; toss. If some of the pieces still look dry, add a little more oil. Sprinkle with salt, toss again, and roast in the oven for 15 minutes undisturbed. When you take it out, you should be able to detach a piece of eggplant without tearing the skin: that's how you know it's time to flip. Flip the eggplant and keep roasting until golden brown all over, at least another 10 minutes. Set aside.
In the meantime, pour a few tablespoons of olive oil into a large Dutch oven. Heat on medium heat and add the red onion with a pinch of salt. Sauté until starting to turn translucent, then add the garlic and continue to cook until fragrant. Add all of the tomatoes, another pinch of salt, some basil, and cook on medium heat just until the tomatoes begin to break down and release their juices. Then add the eggplant and cook on a low simmer.
Bring a pot of water to a boil and season with salt. Add the pasta and cook one minute less than package directions. If the tomato/eggplant looks dry, add a ladleful of the pasta water. When the pasta's ready, lift it with a spider tool into the pot with the eggplant and tomatoes. Crank up the heat and stir everything together until the pasta has absorbed the sauce and the bottom of the pot is relatively dry.
Turn off the heat and after a minute add the mozzarella balls, stirring them in. Let them sit for another minute so they start to melt. Stir again and ladle into pasta bowls and garnish with more basil and Aleppo pepper.
