How to Make It
Preheat oven to 375°F. Cut squash in half lengthwise. Remove and discard seeds. Place squash halves, cut sides down, in a microwave-safe 13- x 9-inch baking dish and add ¼ cup water. Cover dish with plastic wrap and pierce 3 to 4 times with a knife. Microwave on HIGH 10 minutes. Carefully drain water out of dish. Turn squash halves over, and bake in preheated oven until tender, 35 to 40 minutes. Let stand about 5 minutes. Scoop flesh from squash, leaving a ¼-inch-thick shell and transfer to a medium bowl; reserve shells and return to baking dish.
Microwave sweet potatoes on HIGH until tender, 6 to 8 minutes. Let stand until cool enough to handle, about 5 minutes. Peel potatoes and add flesh to bowl with squash along with cream cheese, butter, salt, nutmeg, and pepper; mash with a potato masher or a fork until mostly smooth.
Preheat broiler with oven rack 6 inches from heat. Scoop squash mixture into reserved squash shells and top with cheddar and Parmesan. Broil until golden brown, about 3 minutes. Sprinkle with chives.