Bring a large pot of water to a rolling boil over high heat, and season generously with coarse salt.
Heat ½ cup (100 grams) extra virgin olive oil in a large saute pan over medium high heat. Once hot, add half of the eggplant, and allow to cook, stirring occasionally, until softened and golden brown, about 10 minutes. Remove from the pan, and season to taste with Morton kosher salt. Set aside. Add the remaining ¼ cup (50 grams) extra virgin olive oil and eggplant to the pan, and cook for 10 minutes. Remove from the pan, and season with Morton kosher salt.
Add the eggplant to the simple tomato sauce, and cook over medium high heat for about 3 minutes.
Add the rigatoni pasta to the boiling water, and cook until al dente (still very firm).
Transfer al dente pasta to the tomato sauce, and stir vigorously on high heat until the pasta has slightly softened (it should still have a bite) and the sauce slightly thickens.
Taste and add additional Morton kosher salt and black pepper as needed. Plate and garnish with ricotta salata and optionally basil.