Make the Meat Sauce: Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more. Add ground beef and cook, breaking it up with a spoon, until browned. Drain any excess fat. Stir in crushed tomatoes, tomato paste, beef broth, basil, oregano, salt, and pepper. Bring to a simmer, then reduce heat to low, cover, and cook for at least 30 minutes, stirring occasionally.

Prepare the Béchamel Sauce: In a separate saucepan, melt butter over medium heat. Whisk in flour and cook for 1-2 minutes until a thick paste (roux) forms. Gradually whisk in the milk, a little at a time, ensuring no lumps form. Continue whisking constantly until the sauce thickens and coats the back of a spoon, about 8-10 minutes. Season with salt, pepper, and ground nutmeg. Remove from heat.

Prepare the Cheese Mixture: In a medium bowl, combine ricotta cheese, egg, and 1/2 cup grated Parmesan cheese. Mix well.

Assemble the Lasagna: Preheat oven to 375°F (190°C). Spread a thin layer of meat sauce on the bottom of a 9x13 inch baking dish. Place a layer of lasagna noodles over the sauce. Spread half of the ricotta mixture over the noodles, then layer with about one-third of the shredded mozzarella. Top with another generous layer of meat sauce.

Continue Layers: Add another layer of noodles. Spread with half of the béchamel sauce, then another third of the mozzarella, and another layer of meat sauce.

Final Layer: Place the final layer of noodles. Spread with the remaining béchamel sauce and the remaining mozzarella cheese. Sprinkle with extra Parmesan cheese.

Bake: Cover the baking dish loosely with aluminum foil (you may want to spray the underside of the foil to prevent sticking to the cheese). Bake for 25 minutes. Remove the foil and bake for another 15-20 minutes, or until the cheese is bubbly and golden brown.

Rest and Serve: Let the lasagna rest for at least 10-15 minutes before slicing and serving. This helps the layers set and prevents it from falling apart.