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 chopped zucchini and cook, stirring occasionally, 5 minutes. Add water and simmer, partially covered, until tender, about 15 minutes. Purée soup in 2 batches in a blender (use caution when blending hot liquids). Add the basil into the blender with the last batch of soup, and quickly blend the basil.
Season soup with additional salt and pepper. Garnish with basil leaves or basil flowers.