At least 2 hours before serving, combine the tomatoes, Brie, basil, garlic, the 1 cup olive oil, and salt and pepper in a large bowl. Set aside.
Bring 6 quarts of salted water to a boil in a large pot. Add 1 tablespoon olive oil and the linguine, and boil until tender but still firm, 8-10 minutes.
Drain the pasta and immediately toss with the tomato sauce. Serve at once, passing the peppermill, and the grated Parmigiano-Reggiano cheese if you like.
