Heat the some low calorie cooking spray in a large soup pot or saucepan over medium heat. Add the onion and garlic and sauté for 2-3 minutes until they become translucent.
Add the chopped broccoli and diced potato to the pot. Sauté for another 5 minutes, stirring occasionally. Add a drop of the vegetable stock if it sticks.
Pour in the vegetable stock and add the dried thyme and salt. Bring the mixture to a boil, then reduce the heat to a simmer. Cover the pot and cook for about 15-20 minutes or until the broccoli and potato are tender.
Remove the pot from the heat and allow the soup to cool slightly. Use an immersion blender to blend the soup until smooth. If you don't have an immersion blender, you can carefully transfer the soup in batches to a blender, but be sure to let it cool a bit first.
Return the blended soup to the pot and place it back on low heat. Stir in the fat-free yogurt and cook for an additional 2-3 minutes, stirring continuously. Make sure not to boil the soup after adding the yogurt to prevent curdling.
Season the soup with salt and pepper to taste. Adjust the seasoning as needed.
Serve or allow to cool for future storage.