Melt the butter in a large saucepan over medium heat. Saute onion and garlic until tender. Add the potatoes, chicken stock, thyme, and pepper. Bring to a boil, then reduce heat to low. Cover, and simmer for 20 minutes, or until potatoes are tender.
Transfer about half of the soup to a food processor or blender. Process until smooth, then return to the pot. Stir in milk, and continue cooking until heated through. Season with salt and pepper. Ladle into bowls, and garnish with chopped fresh parsley.