Replacing some of the potatoes with turnips gives this mash a slightly sweet flavor that pairs well with sharp Parmesan. You can also substitute goat cheese, blue cheese, or Cheddar.
Preheat oven to 375 degrees F.
Rub off the excess papery skin from garlic without separating the cloves. Slice the tip off the head, exposing the ends of the cloves. Place the garlic on a piece of foil, drizzle with oil, and wrap into a package. Roast until the garlic is golden brown and soft, about 45 minutes. When cool enough to handle, squeeze the cloves and any oil left in the foil into a small bowl.
Meanwhile, combine potatoes and turnips in a large pot and add enough cold water to cover. Bring to a boil over medium-high heat. Reduce heat to medium-low, cover, and cook until tender, about 20 minutes. Drain.
Return the potatoes and turnips to the pan and place over medium-low heat. Add the roasted garlic and mash with a potato masher to desired consistency. Stir in milk, Parmesan, thyme, chives, butter, salt, and pepper.
Tip: Cut potatoes and turnips into equal-size pieces to ensure even cooking.