Melt butter with the olive oil in a medium saucepan over medium-low heat. Add onions and garlic, sprinkle with salt and pepper, and cook until tender, about 7 minutes.
Add zucchini, and cook until it begins to soften, about 10 minutes.
Add broth, bring to a simmer, and cook until squash is quite soft.
Transfer to a blender and blend until smooth. Taste, add salt and pepper as needed, blending it in before tasting again.
Strain through a fine mesh sieve into a clean pan, and reheat if needed.
Serve, topping with zucchini garnish.