If you make this casserole ahead of time and refrigerate it, cook it for an extra ten minutes with the foil cover on. It freezes well, so make extra for busy days.
Cook the spaghetti in boiling water until al dente. Drain, rinse with cold water to stop the cooking, and set aside.
In a large skillet, heat 2 tablespoons of oil. Then saute the broccoli, cabbage and carrots for 2 minutes. Remove from the pan and set aside in a bowl.
Heat 1/2 teaspoon of oil in the same pan, then add the onion and saute for one minute. Add the meat and stir until brown. Drain off excess fat, then mix in the garlic, oregano and tomato sauce.
Lightly coat a rectangular baking dish with the remaining oil. Place 1/3 of the cooked spaghetti in the bottom of the dish. Spread 1/3 of the vegetables and 1/3 of the meat sauce on top. Sprinkle with 1/3 of both cheeses. Repeat twice, finishing with the cheese. Cover loosely with aluminum foil and bake at 350 degrees for 15 minutes. Then remove the foil and bake for an additional 10 minutes, until the top is brown. Let rest for 10 minutes before serving. Makes 4 to 6 servings.