Place the unpeeled garlic cloves on a baking sheet in a 375 degree oven and roast until soft, about 20 - 30 minutes. Once soft remove the garlic from the peel and set aside.
Bring a saucepan of salted water to a boil. Add the turnips and cook until tender. Once done, drain well.
Place the turnips, butter, roasted garlic, and rosemary in a blender or food processor. Season with salt and pepper. Blend until smooth, scraping down the sides of the blender and adding a little more oil if needed. Season with salt and pepper to taste as needed before serving.