In a food processor, combine the roasted eggplant flesh, roasted garlic, tomatoes, chili pepper, a drizzle of EVOO, salt, pepper and parsley. Puree, transfer to a saucepot and simmer for 20 minutes, then stir in the roasted cherry tomatoes.
Meanwhile, boil water for the pasta. Add salt and the pasta and cook to al dente. Reserve 1 cup of the starchy cooking liquid just before draining. Toss the pasta with the sauce, using the starchy cooking liquid to thin out the sauce.
Dress the basil and arugula with a little lemon juice, EVOO, salt and pepper. Top the pasta with the greens and lots of ricotta salata before serving.