In a food processor, mix the basil leaves, pine nuts, garlic, lemon juice and zest, olive oil at high speed for 2 minutes. Pour the mixture in a bowl and add the pecorino cheese, the parmesan and the salt and pepper to taste; mix well with a spoon, check the seasoning and add a layer of olive oil on top to keep the pesto from drying out or changing color. You can keep the pesto in glass jars in the refrigerator, or freeze it.
Note: The traditional way of serving pesto in Liguria, pesto’s birthplace, is to prepare the pasta with green beans and potatoes, cooking them altogether in the same pot and then mixing them with the pesto sauce before serving. The starch of the potatoes lets the pesto cling to the pasta better.