Preheat oven to 350 degrees F. Line a shallow baking pan with parchment paper or aluminum foil. Cut each squash in half; discard seeds and remove fibrous material. Place halves, cut sides down, in the prepared baking pan. Bake, uncovered, for 40 to 45 minutes or until squash is tender. Let stand until cool enough to handle; slice into 1-inch slices. (If desired, cover and refrigerate overnight. Let the squash come to room temperature before finishing the recipe.) Arrange squash slices in a 2-quart rectangular baking dish, overlapping as necessary.
In a large skillet combine butter, brown sugar, cider, cinnamon, salt, and nutmeg; bring to boiling, stirring to dissolve sugar. Reduce heat and boil gently, uncovered, for 5 minutes or until syrupy. Drizzle glaze over squash. Bake, uncovered, about 10 minutes or until heated through. Spoon glaze over squash before serving.