Step 1: Prepare the Meat Sauce: Heat olive oil in a large pot or Dutch oven over medium-high heat. Add ground beef and Italian sausage, breaking it up with a spoon. Cook until browned, then drain off excess fat. Add chopped onion and cook until softened, about 5 minutes. Stir in minced garlic and cook for 1 minute until fragrant.
Step 2: Stir in crushed tomatoes, tomato sauce, tomato paste, beef broth, fresh parsley, oregano, basil, and red pepper flakes (if using). Season with salt and pepper. Bring to a simmer, then reduce heat to low, cover, and let it cook for at least 30 minutes, or up to 1 hour, stirring occasionally.
Step 3: Make the Béchamel Sauce: In a separate saucepan, melt butter over medium heat. Whisk in flour and cook for 1-2 minutes, forming a roux. Gradually whisk in the warm milk, stirring constantly to prevent lumps. Cook, stirring, until the sauce thickens and coats the back of a spoon, about 5-7 minutes. Season with salt and white pepper. Remove from heat.
Step 4: Prepare the Ricotta Mixture: In a medium bowl, combine ricotta cheese, beaten egg, 1/4 cup Parmesan cheese, and a pinch of nutmeg. Mix well. Season with a little salt and pepper.
Step 5: Assemble the Lasagna: Preheat oven to 375°F (190°C). Spread about 1 cup of meat sauce on the bottom of a 9x13 inch baking dish. Lay 3-4 lasagna noodles over the sauce, slightly overlapping if needed.
Step 6: Spread half of the ricotta mixture evenly over the noodles. Top with about 1.5 cups of meat sauce, then sprinkle with a generous layer of shredded mozzarella.
Step 7: Add another layer of noodles. Spread half of the béchamel sauce over the noodles, then another 1.5 cups of meat sauce, and more mozzarella.
Step 8: Repeat with a final layer of noodles, the remaining ricotta mixture, meat sauce, and all remaining mozzarella. Finish with a sprinkle of Pecorino Romano or Parmesan.
Step 9: Cover the baking dish tightly with aluminum foil (you can spray the underside of the foil with cooking spray to prevent cheese from sticking). Bake for 45 minutes.
Step 10: Remove the foil and bake for an additional 15-20 minutes, or until the cheese is golden brown and bubbly. If desired, you can broil for 2-3 minutes at the end for extra browning, watching carefully to prevent burning.
Step 11: Let the lasagna rest for at least 15-20 minutes before slicing and serving. This allows the layers to set, making for cleaner slices.