In a large saucepan over medium heat, warm the olive oil. Add the onion and sauté until softened, about 5 minutes.
Add the zucchini and season to taste with salt and pepper. Continue to saute until the zucchini and onion are browned, 5-7 minutes longer.
Add the vegetable stock and 2 TBSP of the oregano, and bring to a simmer. Cover and cook until the vegetables are tender, about 15 minutes. Remove the soup from heat.
To make the oregano cream, stir together the sour cream, remaining 1 TSP or oregano, and salt and pepper to taste in a small bowl.
In a blender or food processor, puree the soup in batches until smooth. Return the soup to the pan and reheat it. Adjust the seasoning with salt and pepper to taste.
Ladle the soup into bowls and garnish each bowl with a big spoonful of oregano cream. Serve immediately.