Place the oil in a heavy pot. Add zucchini, onion, lemon zest and a little salt to help draw out the juices. Sweat them, covered, for 25 minutes. Check and stir frequently. Don't let the zucchini brown. Don't overcook it, either, or it will take on an unappetizing olive hue.
When the vegetables are quite tender but not mushy, add the stock. Simmer everything together for 5 minutes.
Using a blender set on high, puree the soup in batches and strain it through a fine strainer or sieve, discarding any fibrous solids. Whisk in buttermilk to taste and chill at least 4 hours.