Combine milk, sweet potatoes, apples, onion, carrots, celery, garlic, salt, nutmeg, cayenne pepper, and peppercorns in a large pot; bring to a boil. Reduce heat to low, cover pot, and simmer, stirring occasionally, until potatoes are soft, 20 to 30 minutes.
Pour soup into a food processor or blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth.
