Bring a pot of salted water to a boil. Cook the pasta according to the package directions for al dente. Drain, toss with some oil and keep warm.
Drain the tomatoes into a large bowl and reserve the juice. Roughly crush the tomatoes with your hands.
Heat 2 tablespoons of the oil in a large skillet over medium-low heat. Add the garlic, anchovies and chile flakes and cook, stirring occasionally, until the garlic is lightly golden, about 3 minutes. Add the crushed tomatoes and a generous pinch each of salt and pepper. Increase the heat to medium-high and bring to a simmer. Cook, stirring occasionally, until the tomatoes are soft and begin to lose their shape, 5 to 7 minutes. Stir in the olives, capers and reserved tomato juice. Continue to simmer until the sauce has thickened slightly and the flavors have blended, about 10 minutes more.
Add the cooked pasta to the skillet along with the parsley and remaining 1 tablespoon oil and toss well. Season with salt and pepper and serve with Parmesan.
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