Coarsely chop tomatoes, reserving juice. In a large bowl combine tomatoes and their juice, vinegar, 3 tablespoons of the extra-virgin olive oil and basil. In a very small skillet heat 1 tablespoon olive oil over medium heat. Saute garlic 3 minutes, without allowing garlic to brown. Scrape garlic and oil into tomato mixture and season to taste with salt and pepper. Marinate tomato sauce at room temperature, 5 to 6 hours.
In a large pot of boiling salted water, cook linguine according to package directions until al dente, 5 to 10 minutes; drain in a large colander. Return pasta to pot and toss with remaining 1 tablespoon extra-virgin olive oil and grated Parmesan; divide among 6 bowls. Using a slotted spoon top each portion with about 1 cup tomato chunks. Ladle remaining tomato liquid around pasta.