Heat the olive oil in a Dutch oven over medium heat then add the onion and cook until softened, about 5 minutes.
Add the zucchini and broth, increase the heat to high and bring to a boil.
Reduce the heat to low, cover and simmer for 15 minutes.
Purée using an immersion blender or purée in two batches in your regular blender and return to pan. (Joan purées only half of the soup because her family likes the chunkier version; I purée all of it.)
Add the nutmeg, basil, salt and pepper, and simmer for 5 minutes.
Add the cream now if using. I start with the smallest amount, stir and taste. My preference is less cream, however, you and your family may like more cream. The soup is also good without any cream at all. This is all up to you!
Soup can be served hot or cold.