Bring 4 quarts water to a boil in a large Dutch oven.
Add 1 tablespoon salt and spaghetti to boiling water; cook 10 minutes or until spaghetti is al dente.
Drain spaghetti in a colander over a bowl, reserving 1/3 cup cooking water. Return spaghetti to pan; set aside, and keep warm.
While spaghetti cooks, combine tomatoes, 1 tablespoon olive oil, vinegar, 3/8 teaspoon salt, and pepper on a jelly-roll pan, tossing well to coat.
Bake tomato mixture at 450 for 10 minutes or until tomatoes are soft and lightly charred in places.
Add tomatoes and any tomato juice to spaghetti in Dutch oven.
Add 3 tablespoons reserved cooking water to jelly-roll pan, scraping pan to loosen browned bits; carefully pour water mixture and remaining 1 tablespoon oil into spaghetti mixture.
Place Dutch oven over medium heat.
Add remaining reserved cooking water, 1 tablespoon at a time, until spaghetti mixture is moist, tossing frequently. Stir in basil and parsley.