Cook the pasta until al dente according to the package directions.
Mash (in this order) the garlic, anchovies and olives using a mortar and pestle, or just chop them finely together. Set aside.
Using a fork, crumble the Parmesan.
Heat the olive oil in a skillet over medium-high heat. Add the red onions and cook until slightly caramelized. Add the tomatoes and cook for a couple of minutes. Pour in the broth or wine and cook for another 2 minutes, then pour in the garlic/anchovy/olive mixture. Stir and continue cooking until the sauce is nice and reduced and wonderful, several minutes. Add salt and pepper to taste.
Drain the pasta and add it to the skillet. Add the crumbled Parmesan and toss to coat the pasta in the sauce. Tear the basil leaves and sprinkle over the top. Serve right out of the skillet.