Heat olive oil in a large pot over medium heat. Add chopped onion and cook for about 5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add cauliflower florets and diced potato. Stir to combine.
Pour in vegetable broth and add salt, black pepper, and thyme. Bring to a gentle boil.
Reduce heat and simmer for 15 to 20 minutes until vegetables are very tender.
Use an immersion blender to blend the soup until smooth and creamy.
Stir in lemon juice and Greek yogurt if using. Adjust seasoning as needed.
Serve warm and garnish with parsley or chives if desired.