Set aside one of the zucchini; trim and coarsely chop the rest.
Cook onion in a large saucepan for about 5 minutes, until softened. Add the garlic and cook for another minute. Stir in the chopped zucchini, salt, and pepper and cook over medium heat, stirring occasionally, for 5 minutes. Add the broth and simmer until zucchini is tender, about 15 minutes.
Pour into a blender (in 2 batches, if necessary) taking care to avoid burns by not filling the blender more than halfway. Add the basil, cashews, and nutritional yeast and blend until smooth.
Return soup to the pot, season with salt and pepper to taste, and keep warm. Shred the remaining zucchini with a spiral slicer, mandolin, or grater. Pour soup into bowls and sprinkle grated zucchini over top.