Spoon a ½ cup layer of ragù on the bottom of the baking dish. Place a pasta sheet on top. There’s no need to cook the pasta in advance. It will cook in the juices of the ragù. Spoon another ½ cup of ragù over the pasta. Distribute ¼ of the mozzarella, ¼ of the chopped eggs, ½ cup of bechamel, and ½ cup of Parmigiano-Reggiano evenly over the tray. Repeat the pasta, ragù, mozzarella, egg, béchamel, and Parmigiano-Reggiano layering three more times. Layer the remaining ragù, mozzarella, bechamel, and Parmigiano-Reggiano over the final pasta layer.