Bring a large pot of water to a boil.
Peel about half the skin from the eggplant in strips. Chop the eggplant into bite-size pieces; sprinkle with salt and drain for a few minutes on paper towels.
In a large skillet, heat 2 tbsp. EVOO over medium-high, two turns of the pan. Add the sausage and cook, stirring, until browned and crumbled, about 3 minutes, then add the onion, celery and garlic. Pat the moisture off the eggplant. Stir the eggplant into the sausage mixture; season with salt and pepper. Partially cover and cook to soften the eggplant, 6 to 8 minutes. Add the tomatoes and basil and simmer the sauce to let the flavors combine, 5 to 7 minutes.
Meanwhile, salt the boiling water and cook the pasta until al dente. Stir about 1 cup of the pasta cooking water into the sauce, then drain the pasta and toss it with the sauce. Adjust the seasoning. Serve in shallow bowls topped with cheese and a drizzle of EVOO.