Add the pine nuts to a small skillet over medium heat and toast until golden brown, approximately 2-3 minutes. Set aside.
In the bowl of a food processor, add 1/2 the pine nuts, 3 cups basil, 2 garlic cloves, 1/2 cup cheese and lemon zest. Process the ingredients for approximately 30 seconds or until the ingredients are finely chopped.
While the food processor is still running on low speed, slowly drizzle in 3/4 cup of olive oil and continue processing until a smooth paste begins to form. Stop the food processor and scrape down the sides of the bowl.
Add the remaining pine nuts, basil, garlic and cheese to the bowl. Pulse the ingredients until finely chopped.
Using a rubber spatula, transfer the pesto sauce to a bowl and stir in the remaining olive oil. Season with salt and pepper, to taste.
Store the basil pesto sauce in an airtight container in the refrigerator for up to 5 days.
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Notes
To keep the pesto sauce from oxidizing, top it with a thin layer of olive oil.