Bring a pot of water to boil. When boiling, season generously with salt and cook the pasta according to package instructions, stirring occasionally, until al dente.
While the water is boiling/pasta is cooking, make the sauce. In a large skillet, heat the olive oil over medium heat, and sauté the garlic, anchovies (if using) and red pepper flakes until garlic is golden and fragrant, about 2 minutes. Add the olives and capers and stir to combine.
Add the crushed tomatoes and lower the heat, bringing to a bare simmer. Cook for about 10 minutes or until the pasta is ready. Season with salt and freshly ground pepper to taste. Add about 2/3 of the parsley and toss to combine.
When pasta is al dente, transfer it to the sauce using tongs. Reserve a little of the cooking water.
Toss the pasta with the sauce, adding a bit of the cooking water if necessary.
Garnish the dish with the remaining chopped parsley and serve immediately, with Parmigiano Reggiano on the side.