Put the basil leaves and walnuts into your food processor and pulse a few times to combine.
Add the cheese, salt, pepper, and garlic, and pulse several times to chop through until everything is very small and combined well.
With the food processor running, use the oil drip top on your food processor to slowly add in the olive oil. This will allow the oil to emulsify, thickening the pesto, and keeping everything sticking together so the oil doesn’t separate. If you prefer the oil to be more separate from the herbs (I like it this way too!) you can just do a quick blend through or even just stir in the oil.