Bring a large pot of salted water to a boil over high heat for the pasta.
Oil a 9x13 pan with olive oil.
Heat a 3 Tbsp of olive oil in a large skillet over medium-high heat.
Add the sausages and toss in the hot oil for 3 to 4 minutes, you want them nicely browned on the outside but still rare on the inside. Put the sausages in the baking dish.
Turn the heat down to medium.
Add 1/3 cup of oil to the skillet and get it hot. Add as many eggplant pieces as you can comfortably fit in a single layer and sprinkle well with salt. Cook, turning, for 7 to 8 minutes, until the eggplant is nice and browned, crisp on the outside and soft on the inside. Use a spatula to put the eggplant into the baking dish with the sausage. Cook the rest of the eggplant pieces, adding more oil to the pan, as needed, and putting the finished eggplant into the baking dish.
Add another 3 Tbsp olive oil to the skillet, then the onion and garlic, and cook for 3 to 4 minutes, until translucent.
Dump the whole can of tomatoes and their juices into a bowl and crush the tomatoes with your hands to break them up; add that to the pan with the basil and cook it down until pulpy and relatively thick. This will take about 15 minutes.
Add the rigatoni to the boiling pasta water, give it a stir, and cook for 6 to 7 minutes, it should be slightly firm as it will cook further in the oven. Ladle out 1/2 cup of the pasta cooking water and reserve; the drain the rigatoni.
Preheat the oven to 450°F.
Chop the sausages into nice big, bite-size chunky pieces and return the pieces to the baking dish. Add the tomato sauce, rigatoni, and the reserved pasta water.
Break up half the mozzarella over the mixture, season with salt and pepper, and gently mix with your hands or a spatula until combined.
Dust with the Parmigiano and drizzle with olive oil. Bake for 15 minutes.
Spread the remaining mozzarella in an even layer over the top and continue to bake for another 10 minutes or until golden brown and bubbly.