Place the zucchini in the food processor fitted with an S-blade and process until smooth.
Add basil, olive oil, nutritional yeast, garlic, and salt and pulse a few times to coarsely chop the basil.
Add the pine nuts and process until the texture is creamy, with crunchy, bits of pine nut throughout. Do not over-process or the pesto will become too oily.
Stored in a sealed glass jar in the refrigerator, your pesto will keep for about 5 days.
Alternatively, pour the sauce into ice cube trays, and once frozen, transfer the single serving pesto cubes to an airtight container in the freezer. Stored in the freezer, you can enjoy fresh Italian pesto goodness all winter long.
Hand chopping with a mezzaluna is the traditional, Italian way of making pesto, and it only takes about 20 minutes. By chopping all the ingredients by hand and not blending them, you avoid the ingredients becoming a completely homogenized emulsion or paste. When you serve a pesto that has been hand chopped, you get definition between ingredients, and bright flavors pop in a way they don't when they've been blended into one.
Using a mezzaluna or sharpened chef's knife, start chopping the zucchini until minced.
Add garlic to the zucchini chopping, along with about 1/3 of the basil leaves.
Once this is loosely chopped, add more basil, chop some more, add the rest of the basil, chop some more. Scrape and chop, gather and chop. At this point the zucchini, basil and garlic should be a very fine mince.
Add the yeast and about half the pine nuts, chop. Add the rest of the pine nuts, chop. In the end you want a chop so fine that you can press all the ingredients into a basil "cake."
Transfer the pesto "cake" to a small bowl (not much bigger than the cake). Cover with the olive oil.
Gently stir the olive oil into the pesto before serving or freezing.