Heat the oil in a large saucepan over medium heat. Cook the onion for 4–5 minutes. Add the beef and break it into small pieces; cook until no pink remains. Stir in the garlic and tomato paste for 1 minute, then add the crushed tomatoes, tomato sauce, oregano, salt and pepper. Simmer uncovered for 20–25 minutes, stirring occasionally, until thick but spreadable.

Meanwhile, heat the oven to 375°F (190°C). Boil the lasagne sheets in a large pot of water according to their package, stopping at al dente. Drain and lay separately on a clean tray so they do not stick. Lightly oil a deep 9-by-13-inch baking dish.

Stir the ricotta, egg, basil and half the Parmesan together. Keep two cups of mozzarella for the internal layers and one cup for the top.

Spread about 1 cup of sauce across the bottom of the dish. Arrange 4 pasta sheets over it, slightly overlapping or trimming to fit. Add half the ricotta mixture, one cup mozzarella and about one-third of the remaining sauce. Repeat with 4 sheets, the remaining ricotta, one cup mozzarella and another third of the sauce. Finish with the final 4 sheets, all remaining sauce, the last cup of mozzarella and the remaining Parmesan. Cover every pasta edge.

Cover with lightly oiled foil, tenting it away from the cheese. Bake for 30 minutes, then uncover and bake another 15–20 minutes, until bubbling and golden. Check the center reaches 165°F (74°C) with a food thermometer; bake longer if needed.

Let rest for 20 minutes before slicing into 8 servings. Garnish with optional basil. Refrigerate leftovers in shallow containers within 2 hours, or within 1 hour if above 90°F.