Chop your garlic cloves quite fine, and set aside.
In a pot or a larger saucepan, heat 2 tablespoons of the olive oil in a pan on low heat.
Add the garlic, chili flakes, and capers to the heated oil. It should sizzle lightly, or start to sizzle within a few minutes. Be sure to stir this every few minutes so that you don't burn the garlic or chili flakes.
While these cook, roughly chop your olives, and then add them to the mix, still keeping everything on low heat and stirring every couple minutes.
Finely chop your anchovy fillets. If you've never used anchovies before, don't be intimidated. Your food will not taste fishy- anchovies just add an extra (amazing!) boost of flavor to the sauce. Once your anchovies are chopped down quite small, add them to the pot and give everything a good stir.
Pour the entire can of tomatoes into a food processor or blender, and pulse very quickly, for about a total of 5 seconds. You don't want the tomatoes to turn into puree- puttanesca should be more chunky and less saucy, with larger bits of tomato.
Add the tomatoes into the pot, along with the reserved anchovy oil and an extra splash of olive oil. Season with (a little bit) of salt to taste, and a few good shakes of black pepper. Gently stir to incorporate everything, and then allow the sauce to simmer gently for about 10-15 minutes.
Meanwhile, boil a pot of water on the stove for your choice of pasta. I prefer linguini or fettuccini, but you can use whatever you'd like. Once the water is boiling, cook until al dente, and strain. Toss gently with olive oil.
Serve the pasta with a scoop of puttanesca on top, and garnish with parmesan and fresh parsley.