Step 1

Dump one 28-oz. can whole peeled tomatoes with juices into a medium bowl; crush tomatoes with your hands. Set aside.

Step 2

Heat ⅓ cup extra-virgin olive oil in a large Dutch oven or other heavy pot over medium-high. Add 1 lb. Japanese or globe eggplant, cut into ½" pieces, and sprinkle with 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Cook, stirring occasionally, until eggplant is softened and golden brown, 6–8 minutes. Transfer to a bowl.

Step 3

Heat remaining 2 Tbsp. extra-virgin olive oil in same pot over medium-high. Cook 3 garlic cloves, thinly sliced, and ½ tsp. crushed red pepper flakes, stirring constantly, until fragrant, about 1 minute. Add 3 Tbsp. double-concentrated tomato paste and cook, stirring, until darkened in color, about 2 minutes. Add 2 Tbsp. coarsely chopped oregano, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and reserved tomatoes. Bring to a boil and cook, stirring occasionally, until sauce is slightly thickened, about 5 minutes. Return eggplant to pot and cook, stirring occasionally, until eggplant is completely tender and flavors have melded, about 2 minutes.

Step 4

Meanwhile, cook 1 lb. tubular pasta (such as calamarata or rigatoni) in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1 cup pasta cooking liquid.

Step 5

Add pasta and ½ cup pasta cooking liquid to sauce. Cook, stirring often and adding more pasta cooking liquid if needed, until sauce is thickened and coats pasta, about 2 minutes.

Step 6

Divide pasta among shallow bowls. Top with 4 oz. ricotta salata, shaved, dividing evenly, and torn basil leaves. Season with freshly ground black pepper.