Trim the ends of the eggplant, then slice into ½-inch (1 ¼ cm) thick rounds. Lay the eggplant rounds on a paper towel and season generously on both sides with salt. Let rest for 10 minutes to draw out excess moisture. After 10 minutes, pat the eggplant rounds with a paper towel to remove the moisture.
Heat a griddle pan over medium-high heat and grease with 2 tablespoons of the olive oil, or your oil of choice. Grill the eggplant for about 2 minutes on each side, or until grill marks are formed. Set aside to cool, then cut into bite-size pieces.
Heat the remaining 2 tablespoons of olive oil in a large pan over medium heat. When the oil is hot, add the smashed garlic and cook until fragrant and lightly browned but not burnt, flipping as needed. Remove the garlic from the oil and set aside to cool, then mince.
To the garlic oil, add the chopped tomatoes. Cook for 5-10 minutes, or until caramelized. Add the reserved tomato juice and simmer until reduced to a sauce-like consistency, 5-8 minutes.
Add ½ teaspoon salt, the red pepper flakes, and the minced fried garlic. Stir well, reduce the heat to low, and simmer while you make the pasta.
In a large pot of boiling water, cook the pasta according to the package instructions. Drain and return to the pot.
Pour the tomato sauce over the hot pasta. Add the eggplant, ricotta salata, and fresh basil. Toss until well combined.
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