Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Reserve about 1 cup of pasta water, then drain the spaghetti in a colander.
In a large skillet, heat the extra-virgin olive oil over medium heat. Add the finely chopped garlic and sauté for about 1-2 minutes until fragrant, being careful not to let it burn.
Stir in the chopped anchovies and cook until they dissolve into the oil. Then, add the canned tomatoes with their puree, Kalamata olives, capers, dried oregano, and dried crushed red pepper. Let it simmer for about 10-15 minutes, allowing the flavors to meld together. If the sauce gets too thick, add a bit of the reserved pasta water.
Once the sauce has thickened, add the drained spaghetti directly into the skillet. Toss to combine, ensuring the pasta is well-coated with the sauce. If needed, add more pasta water to achieve your desired consistency.
Remove the skillet from heat and stir in the chopped fresh parsley. Serve the Spaghetti alla Puttanesca hot, topped with grated Parmesan cheese.