Use tomatoes held at room temperature until fully ripe. Core tomatoes; coarsely chop (makes about 3 cups); set aside.
In 4-quart saucepan heat oil until hot. Add onion and garlic; cook and stir until softened, 3 to 4 minutes. Add beans, broth, 1 cup water, black pepper, Italian seasonings and reserved tomatoes; bring to a boil; reduce heat and simmer, covered 15 minutes.
Stir in spinach; cook until spinach is tender, 2 to 3 minutes.
To serve, in each bowl place a slice of bread; ladle in soup. Sprinkle with Parmesan cheese.