Cook pasta in a large pot of boiling water with salt until barely al dente.
While pasta is cooking, heat oil in a large skillet over medium-high heat. Add red onion, garlic, anchovies, and red bell pepper flakes. Cook, stirring, until garlic is fragrant and onion is slightly caramelized, about 2-4 minutes.
Add tomatoes and their juice, breaking them up by hand. Stir in capers and olives. Bring to a boil; reduce heat. Simmer until thickened, approx 8-10 min. Stir in arugula and simmer for a minute until slightly wilted.
When pasta is done, drain and add to skillet, tossing it with sauce to combine. Top with crumbled cheese and torn basil.