Add diced potatoes, chicken or vegetable broth, dried thyme, salt, and black pepper. Bring to a boil.
Reduce heat to low, cover, and simmer for 15-20 minutes until potatoes are tender.
Using an immersion blender, blend the soup until smooth. Alternatively, transfer the soup in batches to a blender and blend until smooth, then return to the pot.
Stir in milk or cream and heat through (do not boil).
Taste and adjust seasoning if needed.
Serve hot, garnished with chopped fresh parsley if desired. Enjoy!