Add the walnuts, fresh basil leaves, garlic, and a pinch of salt to the bowl of a food processor fitted with the blade attachment.

Pulse the ingredients until the basil leaves are finely chopped, and everything is well combined. At this stage, you want a coarse mixture.

Add the grated Parmigiano Reggiano and Pecorino Romano cheeses to the mixture in the food processor.

Pulse the mixture again until the cheeses are evenly distributed and incorporated into the pesto.

With the food processor running, slowly pour in the fresh lemon juice in a steady stream. This will help brighten up the flavors of the pesto.

While the food processor is still running, slowly stream in the extra virgin olive oil until the pesto reaches a smooth and creamy consistency. You may need to scrape down the sides of the bowl occasionally to ensure everything is well-mixed.

Taste the pesto and adjust the seasoning if needed, adding more salt or pepper to suit your taste preferences. You can also add more olive oil if you prefer a thinner consistency. Use the pesto immediately, or transfer leftover pesto to an airtight container and store it in the refrigerator for up to a week. Enjoy it tossed with pasta, spread on sandwiches or as a flavorful topping for grilled meats and vegetables.