01 - Melt the butter in a large pot over medium heat. Add the onion, carrot, and celery. Sauté for 5 minutes until softened and fragrant.
02 - Stir in the minced garlic and cook for 1 minute until aromatic, being careful not to burn it.
03 - Add the diced potatoes, thyme, nutmeg, vegetable stock, salt, and pepper. Bring to a boil, then reduce heat to low, cover, and simmer for 20-25 minutes until potatoes are completely tender.
04 - Use an immersion blender to puree the soup until completely smooth. For a chunkier texture, blend only partially or leave some pieces intact.
05 - Reduce heat to low. Stir in the milk, heavy cream, grated cheddar cheese, and sour cream. Cook gently for about 5 minutes, stirring constantly, until the cheese is fully melted and the soup is creamy and well combined. Adjust seasoning with salt and pepper as needed.
06 - Ladle the hot soup into serving bowls. Top with additional grated cheddar cheese and freshly chopped chives. Serve immediately while hot.