Coat the bottom of a heavy 6-quart pot with olive oil. Add the onions, carrots, celery, and garlic. Season with salt and pepper. Cover and cook over medium-low heat for 15 minutes, or until vegetables are wilted and aromatic; stirring often.

Uncover, heat to medium high, stir in the tomato paste, basil, and paprika. Cook for 3 minutes, stirring often. Add zucchini, spinach, cabbage, Swiss chard, green beans, tomatoes, and broth. Bring the soup to a simmer, partially cover the pot, and cook 30 minutes, or until the vegetables are tender and soup tastes of deep, satisfying flavors. If it tastes weak, uncover and simmer for 5 minutes or more to boil off some of the liquid and concentrate the soup's flavor.

For each serving, toast a thick slice of bread. Rub with garlic, place a slice in the soup bowl, ladle the hot soup on top and garnish with olive oil and Parmigiano-Reggiano cheese.