Preheat oven to 325° F. Start water for pasta in the 8 quart pot. Cook the pasta while making the sauce.
Saute onions, garlic and pepper in the 4 qt saucepan over medium high heat.
Grate the carrots while the onions cook, then add the carrots to the saucepan. Saute for 2-3 minutes.
Stir in tomatoes. Rinse the beans and add to the sauce. Add olives, mushrooms, and spices and stir.
Thoroughly squeeze the moisture out of the the thawed spinach and add to the sauce.
Drain the cooked pasta.
Ladle some of the sauce into the bottom of the baking pan. Build in layers, starting with 1/2 of the cooked pasta, then 1/2 of the cheese, and some sauce. Layer in the rest of the pasta, some more sauce, and sprinkle the remaining cheese on top. You might have some leftover sauce.
Bake for 15-20 minutes or until cheese is browned on top. Allow to sit 10-15 minutes after removing from oven.