Spread cubed eggplant on a baking sheet and toss with 1 teaspoon kosher salt. Let sit for 15 minutes to draw out moisture, then pat very dry with paper towels. This step prevents sogginess and ensures crisp frying.

In a large skillet, heat 2 tablespoons olive oil over medium-high. Working in batches, add eggplant in a single layer and fry, turning occasionally, until deeply golden and tender, about 6–8 minutes per batch. Transfer to a paper-towel-lined plate.

In the same skillet, lower heat to medium and add remaining 1 tablespoon olive oil. Sauté garlic slices until fragrant but not browned, about 1 minute. Add red pepper flakes if using, then pour in the hand-crushed tomatoes with all their juices.

Season the sauce with a pinch of salt and a few grinds of pepper. Bring to a simmer, then reduce heat to low and cook gently for 20 minutes, stirring occasionally, until thickened and rich. Stir in half the torn basil at the very end.

Meanwhile, bring a large pot of generously salted water to a boil. Cook rigatoni until al dente according to package directions. Reserve 1/2 cup pasta water before draining.

Return the fried eggplant to the sauce and stir gently. Add drained pasta and toss, adding splashes of reserved pasta water as needed to create a glossy, saucy coat. Fold in remaining basil and remove from heat.

Transfer to a warm serving bowl. Generously dust with grated ricotta salata, scatter extra basil on top, and finish with a drizzle of raw olive oil. Serve immediately, passing more cheese at the table.