Preheat your oven to 350°F (175°C). Fill a large pot with water, season with salt, and bring it to a rolling boil. Add the lasagna noodles and cook them according to the package instructions until they are al dente, or slightly firm to the bite. Drain, rinse with cold water to prevent sticking, and set aside.
In a large skillet or Dutch oven over medium-high heat, cook the ground beef, Italian sausage, onion, and garlic until the meat is fully browned and no pink remains. Drain any excess fat to avoid a greasy sauce.
Add the pasta sauce, tomato paste, Italian seasoning, ½ teaspoon salt, and ¼ teaspoon black pepper to the skillet. Stir well and let the mixture simmer uncovered over medium heat for about 5 minutes, allowing the flavors to meld and the sauce to slightly thicken. Taste the sauce, and adjust with additional salt if needed.
In a medium-sized bowl, combine 1 ½ cups of the mozzarella cheese, ¼ cup of the Parmesan cheese, ricotta cheese, parsley, beaten egg, and ¼ teaspoon salt. Mix until smooth and well-blended.
To assemble, spread 1 cup of the meat sauce over the bottom of a 9x13-inch baking dish. Place 3 lasagna noodles over the sauce, then layer with ⅓ of the ricotta cheese mixture and another cup of the meat sauce. Repeat this layering process two more times. Finish with a final layer of 3 noodles topped with the remaining meat sauce.
Cover the dish with aluminum foil and bake in the preheated oven for 45 minutes.
After 45 minutes, remove the foil and sprinkle the top of the lasagna with the remaining 2 ½ cups mozzarella cheese and the remaining ¼ cup Parmesan cheese. Return the lasagna to the oven and bake, uncovered, for an additional 15 minutes, or until the cheese is melted, browned, and bubbly. For a golden finish, broil for 2-3 minutes, watching closely to avoid burning.
Allow the lasagna to rest for at least 15 minutes before slicing and serving, ensuring the layers hold together beautifully.