Toss eggplant cubes with 1 teaspoon salt in a colander; let drain 10 minutes. Pat completely dry. Heat 2 tablespoons olive oil in a large skillet over medium-high. Add eggplant in a single layer and cook undisturbed 4-5 minutes until golden on bottom, then toss and continue cooking 5-6 minutes more until crisp-tender. Transfer to a plate.

In the same skillet, add remaining 1 tablespoon olive oil and garlic; sauté 30 seconds until fragrant. Add crushed tomatoes, red pepper flakes, and a pinch of salt. Simmer vigorously, stirring often, for 10 minutes until thickened and slightly reduced.

Meanwhile, cook pasta in salted boiling water until 1 minute less than al dente according to package directions. Reserve 1 cup pasta water, then drain.

Add the drained pasta and half the reserved pasta water to the tomato sauce. Toss over medium heat, adding more water as needed, until the sauce clings glossy and the pasta finishes cooking, about 2 minutes.

Remove from heat; fold in the fried eggplant, torn basil, and half the ricotta salata. Taste and adjust salt and pepper. Divide among bowls, top with remaining ricotta salata, more basil, and a final drizzle of olive oil.