In a large enameled or other non-reactive saucepan or skillet, heat the oil over medium-high heat. Add the onion and crushed red pepper flakes and saute until tender and beginning to caramelize around the edges, 6 to 8 minutes. Add the garlic and cook 1 to 2 minutes, stirring. Add the tomatoes, olives, capers, and anchovies and bring to a boil. Reduce the heat to low and simmer, uncovered, for 15 to 20 minutes, stirring occasionally, until the sauce has thickened and the flavors have come together. Remove from the heat, taste, and season with salt and pepper, to taste. Add the sugar if the sauce is too acidic, and 1 teaspoon or 2 of the caper juice if the caper component seems lacking.

Bring 5 quarts of salted to a boil in a large saucepan and cook the pasta according to package directions until al dente, 10 to 12 minutes.

Drain the pasta in a large colander. Return to the saucepan and toss the hot pasta with 1/2 of the sauce. Serve with more sauce ladled on top and drizzle with more extra-virgin olive oil, if desired. Garnish with the fresh basil leaves and serve immediately. Pass the cheese at the table for guests to help themselves.