Heat 1/4 cup of olive oil in a large pot over MEDIUM heat. Add the diced onion and cook until translucent.
Add the ground chuck and ground pork, breaking the meat apart with a spoon. Cook until browned.
Stir in the minced garlic and red pepper flakes, cooking for another minute. Pour in the white wine, then add the hand-crushed plum tomatoes. Season with salt and pepper.
Let the sauce simmer for 30 minutes. Finish by stirring in the 5 chopped basil leaves. Set aside.
Preheat your oven to 375°F. In a large pot of salted boiling water, cook the pasta noodles until just shy of al dente. Drain and toss with 3 tablespoons of olive oil to prevent sticking. Let the pasta cool slightly.
In a large bowl, combine the beaten eggs, coarse cracked black pepper, half of the grated Pecorino Romano cheese, and half of the shredded mozzarella. Add the cooled pasta and toss to coat evenly.
In a deep-dish pie pan or a springform pan, layer half of the pasta mixture. Dot with spoonfuls of ricotta cheese and then layer with half of the meat sauce. Sprinkle with a portion of the remaining Pecorino Romano and mozzarella cheeses. Repeat the layers with the remaining pasta, meat sauce, and cheese. Finish by topping with the remaining Pecorino Romano and mozzarella.
Bake in the preheated oven for 25-30 minutes, until the cheese is bubbly and the top is golden brown.
Let the lasagna pie rest for 10 minutes before slicing. Garnish with the chopped basil and minced parsley.