Cook beef in its own fat until beef loses its pink color, stirring to break apart. Drain or skim off excess fat.
Add onions, saute 3 minutes. Add pepper, oregano, thyme, red pepper, garlic, and basil, and cook 5 minutes longer. Add tomatoes and tomato paste to meat mixture. Blend well, simmer 1 hour. Skim off excess fat. Set aside.
Combine eggs, cheeses, and parsley. Mix well and place in shallow pans, refrigerate.
Preheat a convection oven to 300 degrees F and set fan on high with closed vent, or heat a regular oven to 325 degrees F.
In 5 large baking dishes, place 2 1/2 cups meat sauce. Top with noodles in rows. Top with 3 1/2 cups chilled filling. Top with 1 quart meat sauce, more noodles and 3/12 cups chilled filling. Top again with 1 quart meat sauce, noodles, placed in rows and 1 quart meat sauce. Sprinkle 1 ounce Parmesan over each pan.
Cover pans and cook for 1 hour. Uncover and bake for 10 to 15 minutes. It may take slightly longer in the oven if not using a convection oven.