Heat the olive oil in a large pot over medium-high heat. Add the carrots and onion and cook, stirring constantly, until the onion is lightly browned, about 5 minutes. Add the garlic, tomato paste and 1 tablespoon salt and cook 1 more minute. Add 7 cups water, cover and bring to a boil. Uncover, reduce the heat and simmer 5 minutes. Season with salt and pepper.
Meanwhile, trim the green beans and zucchini and cut into 1/2-inch pieces. Stir into the prepared broth along with the beans and spaghetti. Simmer until the pasta is al dente, about 10 minutes.
When ready to serve, whisk 1/3 cup pesto into the soup. Ladle into bowls and top with the remaining pesto. Sprinkle with parmesan and serve with bread, if desired.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine