(Optional) Toast the nuts or seeds for extra flavor: Place the nuts/seeds in a medium skillet over medium heat, stirring frequently (don’t let them burn!), until nice and fragrant, 3 to 5 minutes. Pour them into a bowl to cool for a few minutes.
Combine the basil, cooled nuts/seeds, Parmesan, lemon juice, garlic and salt in a food processor or blender. With the machine running, slowly drizzle in the olive oil. Continue processing until the mixture is well blended but still has some texture, pausing to scrape down the sides as necessary.
Taste, and adjust seasoning if necessary. Add a pinch of salt if to reduce bitterness or add more zing. Add more Parmesan for a creamier/cheesier pesto. Thin it out with more olive oil or if serving with pasta, use reserved pasta cooking water.