01 - Toast walnut halves in a dry skillet over medium heat, stirring frequently, until fragrant and lightly golden, approximately 4 to 5 minutes. Allow to cool slightly.
02 - In a food processor, combine the toasted walnuts, fresh basil leaves, grated Parmesan cheese, lemon zest, lemon juice, and peeled garlic cloves. Pulse until the mixture is finely chopped.
03 - With the food processor running continuously, gradually stream in the extra-virgin olive oil until the pesto achieves a smooth yet slightly textured consistency. Scrape down the sides of the bowl as needed to ensure uniform incorporation.
04 - Season the pesto with fine sea salt and freshly ground black pepper, pulsing briefly to integrate. Taste and adjust seasoning or add more lemon juice if desired.
05 - Serve the pesto immediately, or transfer it to an airtight container and refrigerate for up to 5 days.