Exceptionally good sauce, surprisingly different. Have a try with your gnocchi.
Blend half of the basil, with the garlic, salt, and some of the olive oil.
Then add the parmesan and the pecorino cheese, the rest of the basil, the anchovies and the black olives. Pinenuts at the end. Blend the ingredients together again and it is ready to use.
Serve with some anchovy fillets and black olives aside, if you like. You can keep the pesto in the fridge for next times to use, keep it in a jar topping with extravirgin olive oil.