Add the basil leaves into a food processor along with the walnuts, parmesan cheese, garlic cloves, lemon juice, and salt. Pulse until the ingredients are finely chopped but not quite a paste.
Remove the lid and slowly pour in half of the olive oil, pulsing the ingredients together until they’re mixed well. This step is crucial for achieving that smooth consistency; you want it to be creamy but still have some bits for texture.
For a more liquid-style pesto, add the remaining olive oil and pulse again to mix thoroughly. Watch as the vibrant green color deepens and the texture becomes silkier.
Taste the sauce and adjust the seasoning as desired. This is your moment to make it perfect; whether you need more salt or an extra squeeze of lemon juice, trust your palate!