Heat the olive oil in a large skillet or saucepan over medium heat.
Add the finely chopped garlic and sauté until fragrant, about 1 minute, taking care not to brown it.
Stir in the canned tomatoes with their puree, breaking up large pieces with a spoon.
Add the halved Kalamata olives, chopped anchovy fillets, drained capers, dried oregano, and crushed red pepper; stir to combine.
Reduce heat to medium-low and simmer the sauce, stirring occasionally, until slightly thickened, about 8 minutes; season with salt and pepper to taste.
Meanwhile, bring a large pot of salted water to a boil and cook the spaghetti until al dente according to package instructions.
Drain the pasta in a colander, return it to the pot, then add the sauce and chopped parsley.
Toss the pasta and sauce together over low heat until the noodles are evenly coated, about 3 minutes.
Serve immediately with grated Parmesan cheese on the side.