Chop large onion, garlic and parsley fine and fry slightly in hot oil. Add tomatoes, tomato paste, bay leaves, salt, pepper and water and stir until well mixed. Then toss in the beef, breaking in little pieces with a fork. Cover and cook over low heat for 45 minutes, stirring occasionally.
Chop small onion fine and cook in melted butter a minute or two. Mix in flour smoothly and add Parmesan cheese and a dash of salt. Gradually stir in milk and continue cooking over a low heat, stirring constantly until sauce is thick as heavy cream. Beat egg yolks slightly, mix in a little hot cheese mixture slowly (to prevent curdling). Then mix all cheese mixture and yolks together and cook over low heat for 10 minutes longer. Remove from fire.
Cook noodles as directed on the package, until tender, then drain. Preheat oven to 325 degrees and grease large baking dish. Put layer of noodles and add some cheese sauce on top of tomato sauce. (Optionally, one can add dots of mozzarella and/ or cottage cheese). Repeat this process: noodles, tomato sauce and cheese sauce.
Cook for 45 minutes or until cheese is bubbly.