Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1/2 cup pasta water and drain.

While the water heats, warm the olive oil in a large skillet over medium heat. Add the anchovies and garlic, stirring until the anchovies melt into the oil and the garlic turns golden, about 2 minutes.

Add the crushed tomatoes to the skillet and stir well. Let the sauce simmer until it thickens slightly, about 10 minutes.

Stir in the olives, capers, and red pepper flakes. Season with salt and pepper to taste and simmer for another 2 minutes.

Add the drained pasta to the sauce and toss to coat, adding reserved pasta water as needed to loosen. Serve topped with grated Parmesan.