Heat the olive oil in a large pot, add the onion, and cook for about 4 minutes until softened.
Stir in the garlic, then add the potato, chopped broccoli stems, vegetable broth, thyme, salt, and black pepper.
Bring the mixture to a boil, reduce the heat, and simmer for about 8 minutes.
Add the broccoli florets and continue cooking for another 6 to 8 minutes until all the vegetables are tender.
Blend the soup until smooth, then allow it to cool for a few minutes before adding the dairy ingredients.
Stir in the Greek yogurt, lemon juice, and Parmesan, if using, until evenly combined.
Reheat gently without boiling, taste the seasonings, and serve warm.