3/4 lb Carrots, peeled and

           -shredded
    3/4 lb Turnips, peeled and

           -shredded
    1/2 c  Thinly sliced scallion

           -greens (not bulb)
      2 tb Minced fresh parsley

      4 tb Cornstarch

      2 c  Milk

    1/2 c  Heavy cream, half-and-half

           -OR additional milk
      1 lg Egg

           Salt
           Freshly ground black pepper
    1/2 c  Freshly grated Parmesan

      1 tb Cold unsalted butter, cut

           -into pieces
  Butter a shallow 1 1/2-quart baking dish or a 10-inch round or oval gratin
  dish and set aside. In a large mixing bowl, toss together carrots, turnips,
  scallion greens, parsley and 3 tablspoons of cornstarch. Spread vegetable
  mixture in prepared pan, pressing and smoothing it into place. In a small
  saucepan, dissolve remaiing cornstarch in 1/4 cup of the milk. When
  completely dissolved, add cream and remaining milk. Bring to a boil over
  moderately high heat, whisking constantly.  Reduce to moderate heat. In a
  medium mixing bowl, beat egg with a fork and season with salt and pepper.
  Add egg to milk mixture in slow, steady stream, beating until combined.
  Pour this hot custard over the vegetable mixture in gratin dish. Sprinkle
  top evenly with Parmesan cheese.  (Gratin can be prepared 24 hours ahead to
  this point nad refrigerated.) Dot gratin with butter and make in the middle
  of a preheated 375F oven for 45 minutes, or until it is bubbling through a
  golden crust.  Let gratin stand 10 minutes before serving to crisp crust
  and allow custard to set.