Heat a large, heavy saucepan over medium heat. Add the butter and avocado oil. After butter has melted, stir in the onion. Cook onion until soft and translucent.
Stir in the zucchini squash and oregano. Sprinkle lightly with salt (optional) and pepper. Don't overdo the salt as the feta and the stock will also add saltiness.
Cook the squash until starting to soften, stirring frequently. Add the garlic and cook for about one minute. Pour the stock over.
Cover the pot, leaving the cover slightly off center to allow steam to vent. Simmer until vegetables are soft, about 25 minutes. Stir in the feta cheese and allow to melt slightly. Puree the soup using an immersion blender, or in batches, using a traditional blender.
Stir in the heavy whipping cream and simmer a few minutes. Taste and adjust seasoning if desired. Soup may be thinned with additional stock if desired.