My photos do not show this, but Deborah Madison recommends finishing the soup with bread cubes crisped in a little olive oil and topped with shaved Parmigiano-Reggiano. I urge you to salt to taste as directed, and do not skip adding lemon juice which brightens the soup's flavor considerably.
Warm the oil in a pot with a tight-fitting lid. Add the vegetables, season with ¾ teaspoon salt, then cover the pot and cook over low heat for 30 minutes, during which the vegetables will produce quite a bit of delicious juice. While they are cooking, bring 1 quart water to a boil.
Carefully puree the cooked vegetables with the hot water, beginning with a small amount and adding more, up to 3 or 4 cups, depending on the thickness you want. Leave a little texture or make the soup smooth, as you wish. Return it to the heat, taste for salt, and season with pepper. Add lemon juice to sharpen the flavors.
Crisp the bread cubes in a little olive oil over medium-low heat (or in the oven) until golden, 8 to 10 minutes. Ladle the soup into bowls, drizzle with a little olive oil, and add the croutons. Shave the cheese over the top and serve.