Heat oven to 375°F (190°C). In a large saucepan heat oil over medium heat. Soften onion for 5 minutes; add beef and brown 7–8 minutes, breaking up the meat. Drain excess grease if needed. Add garlic and tomato paste and stir 1 minute.

Add tomatoes, water, oregano, 3/4 teaspoon salt and pepper. Simmer partly covered for 20 minutes, stirring occasionally, until thick but spreadable. Meanwhile boil noodles in a separate large pot of salted water 2 minutes less than package directions; drain and lay flat on an oiled tray.

Mix ricotta, egg, Parmesan, parsley and remaining 1/4 teaspoon salt. Reserve one-third of the mozzarella for the top. Spread about 3/4 cup meat sauce across the base of a 9-by-13-inch baking dish, at least 2 1/2 inches deep.

Layer four noodles, half the ricotta mixture, one-third of the remaining sauce and one-third of the mozzarella. Repeat with four noodles, remaining ricotta and another third each of sauce and mozzarella. Finish with four noodles, remaining sauce and reserved mozzarella. Distribute sauce to the edges so exposed pasta cannot dry out.

Cover with lightly oiled foil without pressing it into the cheese. Bake 35 minutes, uncover and bake 15–20 minutes more, until bubbling throughout, browned on top and 165°F (74°C) in the center. Place a tray below the dish if it is very full.

Rest on a heatproof surface for 15 minutes before slicing into eight portions. This lets the layers settle and makes cleaner slices. The total cooking allowance includes sauce preparation and baking; noodle boiling overlaps with the sauce simmer.