Preheat the oven to 350°F (175°C).
In a large saucepan over medium heat, cook the ground beef until no longer pink, breaking it up as it cooks.
Add salt, black pepper, Italian seasoning, and dried oregano to the beef and stir to combine.
Add the chopped onion and minced garlic to the pan and cook for about 2 minutes, stirring, until the onion softens.
Stir in the crushed tomatoes, bring to a simmer, and cook for 10–12 minutes until the sauce thickens and the onions are tender. Remove from heat.
Spoon 4–5 tablespoons of the meat sauce into the bottom of a 13x9-inch baking dish and spread evenly; set aside.
In a large mixing bowl, combine the ricotta cheese and the egg until smooth. Stir in the spinach.
Reserve 1/2 cup of the mozzarella and 1/2 cup of the Parmesan for topping, then add the remaining mozzarella and Parmesan to the ricotta mixture and stir until thick and well combined.
Cook the oven-ready lasagna noodles according to package instructions until al dente, then transfer them to a large baking sheet to cool slightly.
Place about 2 tablespoons of the cheese-spinach mixture at one end of each noodle and spread into an even layer, leaving the edges clear.
Spoon about 1 tablespoon of the meat sauce over the cheese mixture on each noodle, keeping sauce away from the edges, then roll each noodle tightly and place seam-side down in the prepared baking dish.
Top each roll-up with a little of the remaining cheese mixture and meat sauce, then sprinkle the reserved mozzarella and Parmesan evenly over the rolls.
Cover the dish loosely with foil (avoid touching the cheese) and bake for 30 minutes. Remove the foil and let stand at room temperature for 10 minutes before serving.