Heat the butter with the oil in heavy large saucepan over medium-high heat. Add the onion; sauté until translucent, about 5 minutes. Mix in the garlic and rosemary. Add the broth and potato; bring to boil. Reduce heat and simmer 10 minutes. Add the sliced zucchini; simmer until tender, about 15 minutes.
Working in batches, puree in the blender. Season with salt and pepper.
Cook the cubed zucchini in a saucepan of boiling salted water for 30 seconds. Drain. Re-warm the soup over medium heat. Ladle into bowls. Top with the cubed zucchini and sprinkle with green onions, if desired.
Notes
If preparing this recipe as GLUTEN FREE, just make sure that you use a brand of broth that is designated as GF.