In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the diced potatoes to the pot, followed by the vegetable broth and thyme. Bring to a boil, then reduce the heat and simmer for about 20-25 minutes, or until the potatoes are tender.
Use an immersion blender to puree the soup until smooth. (Alternatively, you can transfer the soup in batches to a blender.)
Stir in the heavy cream and grated Parmesan cheese, mixing until the cheese is melted and the soup is creamy. Season with salt and pepper to taste.
Heat the soup gently, stirring occasionally, until heated through. Do not let it boil after adding the cream.
Serve hot, garnished with chopped chives for a burst of color and flavor.
Notes
For a thicker soup, blend longer or add more potatoes.