About ¾ cup extra virgin olive oil, more for drizzling
5 garlic cloves
4 cups cherry tomatoes, halved
4 sprigs oregano
3 sprigs basil, plus 5 large leaves
5 tablespoons finely grated Parmesan
¼ cup panko bread crumbs
⅓ cup ricotta
2 ounces fresh mozzarella
Step 1 Place the eggplant slices in a colander over a bowl. Season with ½ teaspoon salt. Let stand 20 minutes. Drain and pat slices dry with a paper towel. Season with pepper.
Step 2 Working in batches, heat some of the oil in a large skillet over medium-high heat (you will need about ½ cup total for frying, less with a nonstick pan). Add as much eggplant to the skillet as fits comfortably in a single layer. Cook, without moving, until undersides are dark golden, about 4 minutes; flip and cook 3 to 4 minutes more. Transfer eggplant to a paper towel-lined plate. Repeat with remaining oil and eggplant.
Step 3 Let the skillet cool for a few minutes. Return it to medium heat and add 3 tablespoons oil. Smash and peel 4 garlic cloves and add them to the skillet; cook until golden and fragrant, about 2 minutes. Add tomatoes and oregano. Cook, breaking up the tomatoes with the back of a spatula, until tomatoes start to form a sauce, 15 minutes. Add the basil sprigs and 4 tablespoons Parmesan; simmer 5 minutes longer.
Step 4 While the sauce simmers, in a small skillet over medium heat, warm 1 tablespoon oil. Mince 1 garlic clove and add to the skillet with the bread crumbs. Toast, stirring, until bread crumbs are just golden, about 2 minutes. Remove from heat and stir in 1 tablespoon Parmesan and a pinch of salt.
Step 5 Arrange eggplant on a large platter. Spoon dollops of ricotta over the eggplant and top with sauce. Scatter bread crumbs over sauce. Top with mozzarella and garnish with torn basil leaves. Drizzle with oil and serve.