Start by heating a pan with olive oil. When it gets hot, add anchovy fillets, garlic, and chili, and let them slowly fry for a couple of minutes. Crush the pelati with your hands and add them to the pan, followed by tomato paste, capers, and olives. Turn down the heat and let it cook together until reduced, around 20-30 minutes. The capers will infuse their salt, which should be enough to season the salsa.
Drop your pasta in boiling salted water and cook until al dente. I chose conchiglie from EatWasted, a great project that makes pasta from bread waste in Copenhagen! Drain and add the pasta to the pan.
Turn on the heat and toss the pasta in the sauce, emulsifying with a bit of olive oil and the parsley. Add cooking water if needed to adjust the sauce texture.
Serve immediately and enjoy piping hot.