Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions.
Meanwhile, grate the tomatoes on the largest holes of a box grater into a large bowl, discarding any big pieces of excess tomato skin. Whisk in the oil, basil and 2 teaspoons salt. Stir in the brie.
Drain the pasta, reserving 1/4 cup of the pasta water. Add the pasta to the tomato mixture and toss to combine. Add the pasta water, a little at a time, to moisten the pasta and help the Brie partially melt, if needed.
Top with fresh basil before serving.
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