Cut the zucchini into delicate ribbons with a vegetable peeler or mandolin slicer, being careful to stop peeling once you reach the seeds.
Place the ribbons in a colander and toss with salt. Let stand while you prepare the avocado pesto
Gather the avocado walnut pesto ingredients. This includes avocado, basil, walnuts, garlic, lemon, and cheese.
Add all ingredients into the food processor and blend until the sauce is smooth. Add water to thin the sauce as needed.
Grease a skillet with 1 tablespoon olive oil and bring to medium heat.
Saute zucchini ribbons for 3-5 minutes or until they are just beginning to soften. Remove from heat.
Spoon pesto onto zucchini ribbons and gently toss to coat.
Plate in two portions of fantastically swirled vegetable ribbons. Garnish with fresh basil and grated Parmesan cheese.