Add the walnuts to the bowl of a food processor. Pulse 8–10 times until the walnuts are coarsely chopped into small, pebble-sized pieces. You want some texture here — don't over-process into a powder.

Add the fresh basil leaves (stems removed), freshly grated Parmesan cheese, garlic cloves, lemon juice, lemon zest, salt, and black pepper to the food processor with the chopped walnuts.

Pulse everything together 10–15 times, scraping down the sides of the bowl with a spatula as needed, until the mixture is well combined but still slightly chunky.

With the food processor running on low, slowly stream in the extra-virgin olive oil through the feed tube in a thin, steady stream. Let it run for about 20–30 seconds until the pesto reaches your desired consistency — slightly chunky or silky smooth, your call.

Stop the food processor and taste the pesto. Adjust salt, pepper, or lemon juice to your preference. If it's too thick, drizzle in a little more olive oil and pulse once or twice.

Transfer the pesto to an airtight jar or container. Use immediately, or press a thin layer of olive oil over the top to prevent browning, and store in the refrigerator for up to one week.