Chunky tomato sauce
Bring a small pot of water to boil. While you’re waiting for it to boil, put some ice in a bowl and add water to create a water bath to plunge the hot tomatoes. Once the water comes to a boil, add the tomatoes, one at a time. When the water returns to the boil, count to 10, then remove it and put it in the ice water. Continue until all tomatoes are blanched.
Remove the stem end, and peel the skins from each tomato. Set the tomatoes aside and discard the water bath.
Halve each tomato through the equator. Squeeze each half, discarding the seeds (you can also use a finger to dislodge and dispose of the seeds). Dice the peeled and seeded tomatoes.
In a skillet heated over medium heat, heat the oil, then add the garlic and red chile flakes. As soon as the garlic gives off its aroma and becomes opaque, add the chopped tomatoes, along with the basil and salt. Cover the pan and cook over medium heat until the tomatoes soften and give up their juice, 8 to 10 minutes.
Remove the lid and continue to cook the sauce over medium-high heat, stirring occasionally, until the tomato sauce begins to thicken. If you need to, use a wooden spoon to stir and help break up the tomato pulp. Remove from heat and set the sauce aside while you assemble the eggplant timbale.
Heat the oven to 350 degrees.
Trim the stem and root ends of the eggplants, and cut them lengthwise into 1/3-inch thick slices. Lay the eggplant slices out on paper towels and salt them generously, then set aside until the salt begins to draw moisture from the eggplant (water will begin to bead up on top of the slices), about 15 minutes. Rinse the eggplant slices and dry well using paper towels.
Lightly dredge the slices in flour, shaking off the excess. In a heavy skillet with high sides, pour the olive oil to a depth of 1/4 inch. Heat the oil until it is hot but not smoking.
Fry the eggplant slices in 1 layer, turning once as they brown and adding more oil as necessary. As the slices brown and become tender, remove them, using tongs, to paper towels to drain.
To assemble the timbale, use a 2-quart souffle dish or springform pan. Arrange just enough eggplant slices in an overlapping pattern, radiating from the center, so that the eggplant comes about halfway up the sides, and covers the bottom of the dish. Place more eggplant slices, vertically, in a slightly overlapping fashion(from where the first slices end), up and over the sides of the dish, and overhanging the edge.
6. Cover the bottom layer of eggplant with 3 to 4 tablespoons of the tomato sauce, then sprinkle over a few tablespoons each grated Parmesan and shredded mozzarella. Cover the sauce with a layer of eggplant, cutting the pieces to fit if necessary.
7. Continue layering with sauce, Parmesan, mozzarella and eggplant until all the eggplant slices are used, and ending with eggplant, sauce and Parmesan, no mozzarella.
8. Using a knife, make incisions through the layers of eggplant. Pour the beaten eggs over the layered eggplant, making sure the eggs seep through and around the layers. Fold over the eggplant slices from the sides, to create the final layer.
9. Bake the timbale until the eggs are set and the timbale is bubbling hot, about 40 minutes.
10. Cool the timbale at least 15 minutes before unmolding. Invert the dish onto a serving plate and unmold. Serve at room temperature.