To make vegan, substitute 3 tablespoons nutritional yeast for the Parmesan cheese.
If you want to freeze your basil pesto, leave out the cheese. Portion the cheese-free pesto into an ice cube tray, cover, and freeze. Once frozen, remove the pesto cubes from the tray and store them in a tightly wrapped glass container, or a zip top plastic bag, in the freezer. When you’re ready to use your sauce, defrost a cube or two and add the grated Parmesan.