Boil the pasta: Bring a large pot of well-salted water to a rolling boil.
Add spaghetti and cook until just shy of al dente. Reserve about 1 cup of pasta water before draining.
Warm the oil and anchovies: In a wide skillet, heat olive oil over medium. Add anchovies and stir for 1–2 minutes until they melt into the oil.
This creates the savory base of the sauce.
Bloom the aromatics: Add sliced garlic and red pepper flakes. Cook 30–60 seconds until fragrant. Don’t brown the garlic—lower the heat if it colors too fast.
Add tomatoes: Stir in the crushed tomatoes, then reduce to a gentle simmer.
Cook for 8–10 minutes, stirring occasionally, until slightly thickened.
Fold in olives and capers: Add chopped olives and capers. Simmer another 2–3 minutes so the flavors meld. Taste and adjust salt—remember, the ingredients are naturally salty.
Marry pasta and sauce: Add drained spaghetti to the skillet.
Toss vigorously, adding splashes of reserved pasta water to create a silky, clinging sauce. Aim for glossy, not soupy.
Finish and serve: Off the heat, stir in chopped parsley and lemon zest if using. Grind in black pepper.
Serve immediately with an extra drizzle of olive oil.