1 large or 2 medium eggplants (about 1 1/2 lb.), trimmed, cut into 1/2-inch-thick planks and then 2-inch batons
5 tbsp. EVOO
4 oz. 'nduja
4 cloves garlic, sliced
2 cans (14 oz. each) Italian cherry tomatoes or 3 cups halved fresh cherry tomatoes
1 tbsp. fresh chopped oregano or 1 tsp. dried
1 lb. orecchiette, penne, or short fusilli
Handful of fresh basil, torn
Ricotta salata, coarsely grated, for serving
Arrange eggplant on paper towels and season liberally with salt, then top with another paper towel. Let sit for 20 minutes, then firmly press to release excess liquid. Bring a large pot of water to a boil for the pasta.
In a large lidded skillet or pot, heat 2 tbsp. EVOO, two turns of the pan, over medium. Add the 'nduja and cook, breaking up 'nduja with a wooden spoon until it darkens in color, about 3 minutes. Add the garlic and cook, stirring, 1 to 2 minutes. Add the tomatoes (if using canned, gently crush with a spoon or potato masher to burst; if using fresh, just stir into skillet). Season with the oregano and salt. Cover and cook for 15 minutes, shaking the pan occasionally to keep tomatoes from sticking.
In another nonstick skillet, heat the remaining 3 tbsp. EVOO, three turns of the pan, over medium-high. Add the eggplant and cook, stirring frequently, until lightly browned, 7 to 8 minutes. While tomato sauce and eggplant cook, salt the boiling water and add the pasta. Cook 1 minute less than the package directions. Reserve 1/2 cup of pasta cooking water before draining.
Add eggplant to the tomato sauce and toss. Add the pasta, 1/4 cup of reserved pasta water (plus more if needed), and the basil; toss again. Top with ricotta salata and serve.