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 dried thyme, cooking for an additional minute until fragrant.
Add the diced potatoes and vegetable broth to the pot. Bring to a boil, then reduce the heat to simmer. Cook until the potatoes are tender, around 15-20 minutes.
Once the potatoes are cooked, use an immersion blender to puree the soup until smooth, or carefully transfer in batches to a blender (allow steam to escape).
Return the pureed soup to the pot over low heat, stir in the heavy cream, and heat through. Season with salt and pepper to taste.
Serve hot, garnished with chopped chives or parsley on top.