Warm the olive oil in a large pot over medium heat. Add the onion and minced garlic, and cook, stirring, until the garlic is fragrant and the onions are translucent, about 5 minutes.
Add the lemon zest and zucchini and saute for about 2 minutes. Season to taste with salt and pepper, then add the broth or water and bring to a boil. Lower the heat to a simmer, and cook about 10 minutes, until the zucchini is softened. Stir in the basil until wilted, and remove the pot from the heat.
Using an immersion blender or working in batches in a blender, puree the soup until smooth. Return the soup to the pot, and season with salt and pepper to taste.