Heat the olive oil or butter in a large pot over medium heat. Add the chopped onion and sauté for 5 minutes until translucent and fragrant.

Stir in the minced garlic and cook for another 1-2 minutes, being careful not to burn it.

Add the diced potatoes and dried thyme. Stir to coat everything in the oil and aromatics for about 3 minutes.

Pour in the vegetable broth, bringing the mixture to a boil. Reduce heat to a simmer, cover, and cook for 20-25 minutes until the potatoes are fork-tender.

Using an immersion blender (or transfer to a regular blender in batches), puree the soup until smooth and creamy. If you prefer chunks, blend only half.

Stir in the heavy cream and optional Parmesan cheese. Season with salt and pepper to taste. Simmer for an additional 5 minutes to meld flavors.

Ladle into bowls, garnish with chopped chives or parsley, and serve hot.