Heat 2 tablespoons of olive oil in a large heavy-bottomed skillet or Dutch oven over medium heat. Add the diced onion and cook for 5 to 6 minutes until soft and translucent, then add the minced garlic and stir for 60 to 90 seconds until fragrant.
Increase heat to medium-high and add the ground beef and Italian sausage. Break apart with a wooden spoon and cook for 8 to 10 minutes until no pink remains, then drain off excess fat.
Stir in the tomato paste and cook for 2 to 3 minutes, then pour in the crushed tomatoes and season with oregano, basil, red pepper flakes, sugar, salt, and pepper. Simmer uncovered over low heat for 20 to 25 minutes until thickened, then remove from heat.
In a large mixing bowl, combine the ricotta cheese, eggs, ¼ cup of the Parmesan, fresh parsley, salt, and pepper. Stir until smooth and well combined, then set aside.
Preheat your oven to 375°F (190°C). Lightly grease the bottom and sides of a 9x13-inch deep baking dish with cooking spray or olive oil.
Spread 1 cup of meat sauce on the bottom of the dish, then layer oven-ready noodles, one-third of the ricotta filling, 1 cup mozzarella, and one-third of the sauce. Repeat this layering two more times, finishing with noodles, the remaining sauce (covering noodles completely), the remaining mozzarella, and the reserved ¼ cup Parmesan.
Cover the baking dish tightly with foil (spray the underside lightly with cooking spray to prevent sticking) and bake at 375°F for 45 minutes.
Remove the foil and bake for an additional 20 to 25 minutes until the cheese on top is golden, bubbly, and beginning to brown. A knife inserted in the center should pass through the noodles with no resistance.
Remove the lasagna from the oven and let it rest uncovered for at least 15 minutes before slicing. Use a sharp knife and wide spatula to serve clean, intact portions.