In a large pot, heat the olive oil over medium heat. Add the diced onions and sauté until they are translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced potatoes to the pot along with the vegetable broth and bring to a boil. Reduce heat and let simmer until the potatoes are tender, about 15-20 minutes.
Once the potatoes are cooked, use an immersion blender to puree the soup until smooth. If you prefer a chunkier texture, blend only half of the soup.
Stir in the heavy cream, grated cheddar cheese, thyme, rosemary, and season with salt and pepper. Simmer on low heat until the cheese is melted and the soup is heated through, about 5 minutes.
Taste and adjust seasonings if necessary.
Serve hot, garnished with fresh chives on top for an added burst of flavor and color.
Notes
For a chunkier texture, blend only half of the soup.