Peel the skin off the turnips with a vegetable peeler or paring knife. Discard the skins. Dice the turnips into ¾ inch pieces.
Add the diced turnips to a large saucepan. Place the potato half on top of the turnips. Pour in chicken broth. Then add enough water to the saucepan to cover the turnips and potato. Season with a pinch of salt. Bring to a boil and let cook until turnips have softened enough for a fork to easily pierce through. (about 20 minutes)
Drain the cooking water and discard the potato. Return the cooked turnips to the pot and place back on the stove top over medium heat. Dry cook the turnips over the stove top until most of the remaining moisture is gone.
Transfer turnips to a food processor or blender. Add butter, heavy cream and pepper. Pulse until pureed until smooth and creamy. Season with more salt if needed.
