Heat oil in 3 to 4-quart heavy saucepan over medium-low heat. Add onion, and cook, stirring occasionally, until softened and browned, about 5 minutes. Add salt and garlic and cook an additional 5 minutes.
Add zucchini and cook, stirring occasionally, 5 minutes. Add water and simmer, partially covered, until tender, about 15 minutes. Purée soup with basil in 2 batches in a blender (use caution when blending hot liquids).
Season soup with salt and pepper, and serve hot. Garnish with basil leaves or basil flowers.