In a food processor, combine the basil, Pecorino Romano, Parmesan, pine nuts, garlic, salt, and pepper. Pulse until coarsely chopped.
Slowly stream in the olive oil while the food processor is running, until the mixture becomes a smooth paste. If the mixture is too thick, you can add a bit more olive oil to achieve the desired consistency.
Taste and adjust seasoning as needed.
Use immediately or transfer to an airtight container and store in the refrigerator for up to 3 days.
Pesto Genovese is typically served with pasta, but it can also be used as a spread for sandwiches or as a sauce for chicken or fish.