Heat the oil in a large saucepan over a medium heat. Add the garlic, basil, and zucchini, season to taste with salt, and cook for 10 minutes, until soft. Reserve some of the zucchini pieces to garnish.
Add the stock and simmer for 5 minutes, uncovered, then add the milk and bring just to a simmer. Season with pepper.
Transfer the soup to a food processor and process until smooth, then return to the pan and stir in the Parmesan cheese.
Divide the soup among warmed bowls. Garnish with the reserved zucchini pieces, Parmesan cheese, and a swirl of cream. Serve immediately.