Heat the butter in a medium saucepan over medium heat. Add the onion and cook, stirring, until tender, 3 to 5 minutes. Add the potato, garlic, rosemary, thyme, nutmeg, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring, until the potatoes are well coated, 2 to 3 minutes more. Pour in the stock and bring to a simmer.
Add the sweet potato and turnip and simmer until the vegetables are tender, about 20 minutes, adjusting the heat as needed to maintain a simmer. Remove from the heat and cool at least 5 minutes. Remove and discard the herbs and carefully puree until smooth with a handheld immersion blender or in 2 to 3 batches in a blender (do not fill the blender more than halfway full per batch).
Stir in the cream and reheat the soup if necessary, adjusting the consistency and seasoning with water, salt and pepper.
Serve hot sprinkled with grated Parmesan.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
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