Heat oil in a large pot. At medium-low heat, sauté the onions and eggplant for 10-15 minutes. Add mushrooms and cook another 10 minutes. Add the tomatoes, olives, bay leaves and cayenne. Bring to a boil and reduce heat to low, cook for 30 minutes uncovered.
Add peppers, zucchini, garlic and basil. Salt and pepper. Cook 10-15 minutes longer.
Serve hot over pasta or polenta. Top with grated cheese. Can also be eaten cold.