- 6 oz plum tomatoes (2 or 3 medium)
- 2 tablespoons extra-virgin olive oil plus additional for serving
- 1 small onion, chopped
- 1 large yellow-fleshed potato such as Yukon Gold (1/2 lb)
- 2 medium zucchini (3/4 lb total), quartered lengthwise, then cut crosswise into 3/4-inch pieces
- 1 celery rib, cut into 1/2-inch pieces
- 3 1/2 cups water
- 1 1/2 tablespoons chopped fresh basil
- 1 1/2 tablespoons chopped fresh flat-leaf parsley
- 1 teaspoon dried oregano, crumbled
- 1 1/4 teaspoons coarse gray sea salt
- 1/4 teaspoon coarsely ground black pepper
- 1 large egg
- 2 tablespoons finely grated Parmigiano-Reggiano plus additional for serving
- Cut a shallow X in bottom of each tomato with a sharp paring knife and blanch tomatoes in a 2- to 3-quart saucepan of boiling water 20 seconds. Transfer tomatoes with a slotted spoon to a cutting board and, when cool enough to handle, peel, beginning from scored end, with knife, then seed and chop.
- Heat oil in a 4-quart heavy pot over moderately high heat until hot but not smoking. Add onion and tomatoes, then reduce heat to moderate and cook, stirring occasionally, until onion is softened, 4 to 5 minutes.
- Meanwhile, peel potato and cut into 1/4-inch dice.
- Add potato to onion mixture along with zucchini and celery and cook, stirring occasionally, 5 minutes. Add water, herbs, sea salt, and pepper and bring to a boil, uncovered. Reduce heat and simmer, uncovered, stirring occasionally, until vegetables are very tender, 30 to 35 minutes. Remove from heat.
- Whisk together egg and cheese in a bowl until combined well, then add to soup in a stream, stirring. Divide among 4 bowls and serve with olive oil and cheese.