Bring a large pot of water to a boil. Add some salt and the spaghetti, and cook until just shy of al dente (it will continue to cook in the sauce for a minute or two). Drain, reserving a ladleful of the pasta cooking water.
While the pasta is working, heat the EVOO, 4 turns of the pan, in a large, deep skillet over medium heat. Add the garlic and anchovies, and cook, stirring with a wooden spoon, until the garlic is tender and the anchovies are melted, about 5 minutes.
In a food processor, puree the peppers then add the pepper puree into the garlic-anchovy oil. Warm through and season with pepper to taste.