Bring a large pot of salted water to boil. Cook the spaghetti according to the package directions, save about 1 cup of the pasta water, drain the spaghetti, rinse with hot water, and set aside.
Meanwhile, make the sauce. Heat the olive oil in a large skillet. Add the anchovy paste, garlic, and Calabrian chiles and cook, stirring, for 2 – 3 minutes or until very fragrant. Add the cherry tomatoes, Italian seasoning, 1 teaspoon salt, and pepper, and cook until they start to break down, about 5 minutes. Add the tomato paste and cook, stirring for 2 minutes. Add the tomato sauce, bring to a boil, and cook, uncovered for 10 minutes. Add the pine nuts, raisins, and olives and cook, uncovered for another 10 minutes. Taste, add salt and pepper if needed. Add the spaghetti to the sauce and stir to coat. Add some pasta water if needed to thin the sauce.
Serve the pasta with chopped parsley, a drizzle of olive oil, and grated cheese.