Heat the olive oil in large saucepan over medium heat. Add the onion, broccoli stems and sweet potato and cook, stirring, for 5 minutes.
Add the stock and additional 2 cups (480ml) of cold water. Bring to the boil, then reduce the heat to low, and add broccoli florets. Cook for 15 minutes or until the sweet potato has softened.
Set aside to cool slightly, then use a hand-blender to blend the soup until smooth.
Divide the soup between 4 serving bowls, top with yogurt and gently swirl. Season to taste and serve immediately.