Heat the oil and butter in a large saucepan until foaming. Add the onion and cook gently for 5 minutes, stirring frequently, until softened but not brown.
Add the zucchini and oregano with salt and pepper to taste. Cook over medium heat for 10 minutes, stirring frequently. Pour in the stock and bring to boil, stirring.
Lower the heat, half-cover the pan and simmer gently, stirring occasionally, for about 30 minutes. Stir in the diced dolcelatte until melted.
Process the soup in the blender or food processor until smooth, then press through a sieve into a clean pan.
Add two-thirds of the cream and stir over low heat until hot but not boiling. Add more stock or water if the soup is too thick. Season with salt and pepper. Pour into heated bowls. Swirl in the reamaining cream. Serve, garnish with oregano, extra cheese, cream, and pepper.