Heat the oven to 375°F and grease a 9-by-13-inch dish. Boil the noodles 2 minutes short of package directions, drain and lay flat.
Brown the beef and onion in a skillet and drain. Add garlic and tomato paste for 1 minute, then stir in crushed tomatoes, basil, oregano, 3/4 teaspoon salt and pepper and simmer 10 minutes.
Mix the ricotta, egg, remaining salt, 1 cup mozzarella and Parmesan.
Layer one-third sauce, four noodles, half the ricotta mixture and another third sauce. Repeat with four noodles and remaining ricotta, then finish with noodles, sauce and remaining mozzarella.
Cover with foil and bake 30 minutes. Uncover and bake 12 to 15 minutes more, then rest 15 minutes before cutting.