At least 2 hours before serving, combine the tomatoes, Brie, basil, garlic, the 1 cup olive oil, and ½ teaspoon each salt and pepper in a large serving bowl.
Bring 6 quarts 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 to 10 minutes.