In a blender or food processor, puree the tomatoes to a smooth, creamy consistency.
Add the olive oil to a large pan over medium heat. Once hot, add the anchovies and onions and saute until the onions are soft and the anchovies have melted into the onions. Toss in the capers and garlic, and if you'd like to make the sauce spicier, add a pinch of red pepper flakes. Saute until the garlic is fragrant.
Add the tomatoes and season with salt and pepper. Bring to a simmer and simmer on a medium-low flame for about 30 minutes. Strive for balance in the consistency of the sauce; it has to be fluid but it should not look overly wet. A few minutes before taking the sauce off the fire, add half the basil and more salt and pepper if needed. Garnish with the remaining basil just before serving.