Slice the eggplants into 1 cm / 0.4-inch rounds. Layer them in a colander, salting each layer generously, and let sit for 30 minutes to draw out the bitter liquid.

Rinse the eggplant slices under cold water and pat them completely dry with a kitchen towel.

Heat the frying oil in a 30 cm / 12-inch skillet over medium-high. Fry the eggplant in batches, 2 to 3 minutes per side, until golden brown, then drain on paper towels.

In the same skillet, wipe out excess oil and add 2 tbsp fresh olive oil. Cook the onion, carrot, and celery over medium heat for 6 to 8 minutes until soft and pale gold.

Add the ground beef and ground pork, breaking it up with a wooden spoon, and cook for 8 minutes until no pink remains.

Pour in the red wine and simmer 2 minutes to cook off the alcohol. Stir in the passata, basil, salt, and pepper.

Simmer the ragu uncovered for 35 to 40 minutes, stirring occasionally, until it thickens enough to coat the back of a spoon.

Bring a large pot of salted water to a boil and cook the pasta 2 to 3 minutes less than the package directs. Drain and toss with a small ladle of ragu so it doesn't stick.

Heat the oven to 190 C / 375 F. Grease a 33 x 23 cm / 9 x 13-inch baking dish with the butter.

Spread half the pasta in the dish. Layer with half the fried eggplant, half the ragu, half the sliced eggs, and half the caciocavallo.

Repeat the layers with the remaining pasta, eggplant, ragu, eggs, and caciocavallo. Scatter the breadcrumbs and grated pecorino evenly over the top.

Bake for 30 to 35 minutes, until the top is golden and the edges are bubbling. Rest 10 minutes before cutting into squares.