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 the chopped onion and minced garlic to the pan; cook 2 minutes until fragrant and the onion begins to soften.
Stir in salt, black pepper, Italian seasoning, and dried oregano, then add the crushed tomatoes. Simmer the sauce 10–12 minutes until the onions are soft; remove from heat.
Spoon 4–5 tablespoons of the meat sauce into the bottom of a 13 x 9-inch baking dish and spread evenly; set aside.
In a large bowl, combine 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 the topping, then add the remaining mozzarella and Parmesan to the ricotta mixture and stir until thick and combined.
Cook the oven-ready lasagna noodles according to package directions until al dente. Drain and lay them flat on a baking sheet.
Spoon about 2 tablespoons of the cheese mixture onto each noodle and spread evenly with a spoon or offset spatula, leaving a small border at the edges.
Spoon about 1 tablespoon of meat sauce over the cheese on each noodle, keeping the sauce away from the edges, then roll each noodle tightly and place seam-side down in the prepared baking dish.
Spoon any remaining cheese mixture and meat sauce over the assembled roll-ups, then sprinkle the reserved mozzarella and Parmesan evenly on top.
Cover loosely with foil (not touching the cheese) and bake 30 minutes. Remove the foil and let stand at room temperature for 10 minutes before serving.