First, I recommend salting your eggplant to reduce bitterness, but you can skip this step if you are in a hurry. Slice the eggplant into medium rounds. Arrange the rounds on paper towels or clean tea towels, and salt generously on both sides. Cover with another layer of towels and weigh down (for example, lay a large sheet pan over the eggplant and add canned goods, or heavy cookware, to press down). Allow the eggplant to sit for 30 minutes to draw out moisture. Move on to the next steps while you wait.
Step 2
Heat olive oil in a heavy pan (you will need at least ½ cup, 120mL, to fry the entire eggplant). Add the eggplant rounds and fry on each side until browned and completely soft, adding more olive oil as needed. Do not undercook. As the rounds finish cooking, transfer to a shallow dish. Do not drain.
Step 3
When all the eggplant has been cooked, there should be a few tablespoons of oil left in the pan (if not, add around 3 tablespoons). Remove from the heat and add the chiles and garlic, stirring to cook in the residual heat. Cook until the garlic has just begun to soften, but do not allow it to brown or burn.
Step 4
Add the tomatoes and dried basil, and stir to combine. Gently simmer over medium-low heat for 30 minutes, stirring occasionally.
Step 5
Now preheat your oven to 325°F (165°C). While the sauce simmers, make the pasta. Boil in a large pot of salted water and cook 2-3 minutes short of al dente. Drain, rinsing with cold water to stop the cooking.
Step 6
Once the sauce has simmered for 30 minutes, season to taste with salt and balsamic vinegar. Roughly chop the eggplant and add to the sauce. Toss the sauce with the cooked rigatoni and transfer to a medium casserole dish, adding in cubes of mozzarella if desired.
Step 7
Sprinkle the shredded mozzarella and Parmigiano-Reggiano over the top and cover tightly with foil. Bake for 45 minutes. Remove foil and place under the broiler for 2-3 minutes or until nicely browned. Serve hot, topped with fresh basil or parsley.