-
Combine tomatoes and onions in a large stockpot over medium. Cook, stirring constantly, until tomatoes begin to release their juices, about 5 minutes. Cover and cook, stirring occasionally, until tomatoes are fully broken down and very soft, about 30 minutes.
-
Using a spider or slotted spoon, transfer tomatoes and onions to a large heatproof bowl; reserve liquid in pot. Place a food mill over stockpot. Pass tomatoes and onions through food mill into stockpot, discarding tomato skins and other solids. Stir in fine sea salt, and reduce heat to medium-low. Cover partially, and cook, stirring occasionally, until thickened and reduced to 7 cups, about 1 hour and 15 minutes. Stir in basil leaves; cook 5 more minutes. Remove from heat, and cover to keep warm.
-
While tomato sauce cooks, heat corn oil in a high-sided skillet or large Dutch oven over medium-high, about 5 minutes. Add 3 to 4 cups eggplant to skillet in a single layer. (Eggplant should be almost fully submerged in oil.) Sprinkle with 1 teaspoon non-iodized salt. Fry, stirring occasionally, until eggplant cubes are golden brown and soft to the touch with a crispy exterior, 8 to 10 minutes. Using a spider or slotted spoon, transfer eggplant to a large plate to drain; reserve drained oil. Repeat with a second batch of eggplant and 1/2 teaspoon non-iodized salt. Repeat with a third batch of eggplant and 1/4 teaspoon non-iodized salt. Fry remaining eggplant, in batches if needed, adding 1/8 teaspoon non-iodized salt to each batch.
-
Cook pasta in a large pot of salted water according to package directions for al dente. Drain. Add pasta to tomato sauce, and stir to coat. Fold in fried eggplant and drained oil.
-
To serve, transfer pasta to a rimmed platter or large shallow bowl. Top with ricotta salata, and garnish with fresh basil leaves.