Heat the oil from the anchovy fillets in a heavy large deep skillet over medium-high heat. Add the Italian sausage and break apart with a spoon. Cook until beginning to brown and crisp, stirring often, about 7 to 10 minutes.
Add the anchovy fillets and garlic; stir for 1 minute.
Add the crushed tomatoes, green olives, capers, smoked paprika, and dried oregano. Simmer the sauce for 5 minutes to blend the flavors.
Meanwhile, cook the spaghetti in boiling salted water until just tender but still firm to the bite.
Drain the pasta; divide among plates. Top with the sauce and garnish with grated Parmesan cheese, if desired.
