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. For this step I used an immersion blender stick.
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.