Peel and finely chop the onion and garlic, then sauté them in a deep, heavy-bottomed frying pan with the olive oil. When they begin to brown add the meat and season with salt and pepper, stirring frequently. Let it brown well, then add the peeled tomatoes, squash them with a wooden spoon and mix them with the meat. Lower the heat and simmer for roughly half an hour. In the meanwhile wash the aubergines, cut off the ends and slice them, thinly, lengthwise. Heat a grill pan (or a heavy-bottomed frying pan) and, when it’s scorching hot, place the slices of aubergine on it, sprinkle with salt and drizzle with balsamic vinegar. When they have browned on one side, turn them over and season again with salt. As they become grilled on both sides, place them on a serving dish. Cook the rigatoni in plenty of boiling, salted water, strain them when they’re very “al dente” and tip them into the frying pan with the meat sauce. Add the chopped basil and toss the pasta for a few seconds; let it mix well with the sauce, then turn off the heat and set aside. Line the bottom and sides of an oven dish, about 30 cm in diameter, with the slices of grilled aubergine (leave a few to cover the top at the end); make sure that the slices are half in the mould, with the other half spilling out over the edge. Tip in the pasta mixed with the sauce, spread it out evenly over the entire surface, sprinkle with grated pecorino, and arrange the mozzarella and ricotta (both roughly broken up by hand) on top. Close your timbale with the slices of aubergine you set aside, and then fold the slices protruding out of the oven dish in on top of the filling. Bake in a preheated oven, at 180 °C, for roughly 25 minutes. When it’s cooked, leave the timbale to cool for at least 15 minutes before serving.