Step 1Heat the oven to 350 degrees. In a small sauce pan, bring the cream and star anise to a boil, then remove from heat. Set aside to cool to room temperature.
Step 2While the cream cools, peel the turnips and potatoes and cut each crosswise into slices one-eighth inch thick. Place the sliced turnips and potatoes in separate bowls. Strain and discard the star anise from the cream. Divide the cream evenly, pouring it over the turnips and potatoes, tossing to coat.
Step 3Butter or grease a 9-by-13-inch baking dish. Arrange one layer of the potatoes in the bottom of the dish, overlapping them slightly (you might not use all of the potatoes; reserve any extra for an additional layer). Season with one-half teaspoon salt and one-eighth teaspoon pepper. Repeat with a layer of turnips and season with the remaining salt and pepper. Continue with an additional layer of potatoes if any are left, but do not season.
Step 4Pour the cream from the bowls over the vegetables and cover the dish with foil. Bake, covered, for 45 minutes.
Step 5Remove the foil cover and continue baking until the top layer of vegetables is browned, 15 to 25 minutes. Remove and cool slightly before serving.