1. Arrange as many slices of eggplant as will fit in a single layer on a large baking sheet.  Sprinkle with about 1 teaspoon of kosher salt. Continue layering and salting the slices until all the eggplant is salted.  (You can also do this with multiple baking sheets. I usually use 2 baking sheets to roast the eggplant in the oven, so I typically use both in this step as well. You may still have multiple layers on each sheet.) Set aside for 30 minutes. 

2. Preheat the oven to 425° Fahrenheit.

3. While the eggplant is doing its thing, prepare the sauce. Using the side of a chef’s knife, smash the garlic and peel. In a medium saucepot, add the oil and garlic. Warm over medium-low heat until the garlic is fragrant, about 3 minutes. Pour in the canned tomatoes. Using the back of a wooden spoon, break up the tomatoes. Season with the oregano, ½ teaspoon salt, and a few grinds of black pepper.  Bring to a gentle simmer. Cook, stirring frequently, for about 30 minutes until slightly thickened.  Taste and adjust seasonings, if necessary. (Be careful to not make the sauce too salty as the cheese will add more salt to the finished dish.)

4. Transfer the eggplant slices to paper towels. Blot the slices to remove as much of the water as possible.  Rinse and dry the baking sheets. Drizzle about 3 tablespoons of olive oil on each baking sheet. Arrange as many eggplant slices as possible in a single layer on each sheet. (You will need to do this in batches as there will be more slices than can fit on the 2 baking sheets.) Drizzle the slices with 2 more tablespoons of olive oil.  Place the baking sheets in the oven and roast until the eggplant slices are browned underneath, about 15 minutes. Using a spatula, flip the eggplant slices and roast for an additional 10 minutes until browned underneath on the second side. (I rotate my trays from the bottom to the top rack when I flip them.) These times may vary depending on the thickness of your eggplant slices – so keep an eye on them after the first ten minutes of roasting. Remove from oven and transfer the roasted eggplant slices to a wire rack. Repeat the process until all the eggplant slices are roasted. 

5. Reduce the oven temperature to 350°F. 

6. In a 2 or 3-quart baking dish (see note below), ladle a small amount of sauce to cover the bottom of the dish. Cover the sauce with a single layer of eggplant. Ladle a little sauce over the slices, spreading it evenly across the eggplant. Sprinkle with some mozzarella, about 1 tablespoon of the grated Pecorino, and a few grinds of black pepper.  Top with a few torn basil leaves. Repeat this process until you’ve used all the eggplant. 

7. Top the last layer with about 1/3 cup tomato sauce, mozzarella, and grated Pecorino.  Drizzle the top layer with extra virgin olive oil. (Reserve any remaining sauce for another use.) 

8. Bake, uncovered, until hot and the sauce is bubbling, and the cheese is melted and browned in spots, about 30-40 minutes depending on the size of your baking dish.  (Start keeping an eye on it around 30 minutes.) 

9. If you’d like the top with a bit more color, run the dish under the broiler for a few minutes. (Be sure to watch closely!) 

10. Remove and let rest for about 10 minutes.  Serve and enjoy!