Using a mandoline, slice the turnips crosswise 1/8 inch thick. Arrange half of the turnip slices in the prepared baking dish, overlapping them slightly. Pour half of the cream mixture over the turnips and sprinkle 1/4 cup of the grated cheese on top. Repeat with the remaining turnip slices and cream. Cover tightly with foil and bake for about 1 hour and 15 minutes, until the turnips are tender.