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In a large saucepan, heat 4 tablespoons of the olive oil and sauté the onion and carrot for 5 minutes until soft, stirring occasionally with a wooden spoon.
Add the pancetta with the ground pork and rosemary and cook, stirring continuously, until colored all over, about 5 minutes.
Pour in the tomatoes, season with salt and pepper, and cook over medium heat for an additional 15 minutes, stirring occasionally. Let cool to room temperature.
Meanwhile, cook the pasta in a large pot of boiling salted water until al dente. Drain and add to the meat sauce. Stir well and let cool.
Preheat the oven to 350°F.
Break the eggs into the pan of cooled pasta and sauce, then add the grated Parmesan. Mix together.
Brush the remaining oil over the side and base of an 81/2-inch round nonstick baking dish with sides about 2 inches deep. Pour in the pasta mixture and spread out evenly.
Cook in the center of the preheated oven for 20 minutes until crispy and set.
Once cooked, let rest for 5 minutes -- it will be easier to cut and serve, as the layers will hold together. Serve hot or cold.