In a large bowl, combine the squash, salt, pepper, nutmeg and 1 tablespoon oil; toss to coat. Transfer to a greased 11x7-in. baking dish; pour cream over top.
Cover and bake at 325° for 30 minutes. In a small bowl, toss apples in remaining oil. Spoon over squash. Bake, uncovered, for 25-30 minutes or until squash is tender. Sprinkle with cheese; bake 3-5 minutes longer or until cheese is melted. Freeze option: Before adding cheese, cool baked casserole; cover and freeze. To use, partially thaw in refrigerator overnight. Remove from refrigerator 30 minutes before baking. Preheat oven to 325°. Reheat casserole, increasing time as necessary for a thermometer inserted in center to read 165°. Sprinkle with cheese and bake until melted.