Add to pot the parsnips, apples, potato, veggie broth, and 1 cup water. Bring to a boil; reduce heat and simmer, partially covered, until vegetables are tender, 15-20 minutes.
Using an immersion blender, puree until creamy and smooth (or working in batches, puree soup in a blender until smooth. Return the soup puree to pot.)
Stir in half-n-half. Season with the salt, pepper, and a dash of nutmeg. Taste and adjust seasoning if necessary.
Ladle into bowls and garnish with sliced apple, a small sprinkle of nutmeg, and thyme sprigs.