In a 3-quart saucepan, heat the butter and oil. Add onion and sauté over low heat, stirring occasionally, until translucent. Add the zucchini and continue sautéing for 2 minutes.
Add the broth and 2 tablespoons oregano and bring to a simmer. Cover and cook for 30 minutes, or until tender.
For a coarse texture, pulse the soup in a food processor fitted with the steel blade. For a fine texture, puree in a blender.
Return the soup to the saucepan to heat up again. Add salt and pepper. Add the half and half. Taste for any additional needed seasoning. Garnish with a little bit of oregano and serve.
Notes
In the summertime, you can serve this soup chilled rather than hot. Don't add the half and half. Chill after processing and serve with a dollop of nonfat plain yogurt.
If preparing this recipe as GLUTEN FREE, just be sure to use a brand of broth that is designated as GF.