Place the nuts, cheese, greens, garlic, and 2 tablespoons lemon juice in the bowl of a food processor. Season with pepper to taste and a few pinches sea salt.
Pulse in quick on/off bursts until the mixture is finely chopped but not completely puréed, about 15 times. Scrape down the processor and pulse again to incorporate any larger leaves necessary.
In the feed tube in the top of the food processor, add the olive oil and combine, being careful not to over puree the mixture. Stir in more salt and pepper to taste if necessary. Store in a glass jar in the refrigerator for about a week; add a thin layer of olive oil on top of the pesto to keep it from oxidizing.
Note: Can be frozen in ice cube trays or glass containers.