Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet or line with aluminum foil.
Place squash, cut sides down, on the prepared baking sheet.
Bake in the preheated oven until tender, about 1 hour. Flip squash halves over and set aside to cool.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Add celery, mushrooms, and onion; cook and stir until celery is softened, 5 to 10 minutes. Remove skillet from heat.
Beat egg in a large bowl; stir in sour cream and Parmesan cheese. Stir cheese mixture into sausage mixture. Fill squash halves with sausage filling.
Bake in the preheated oven until filling is cooked through, about 20 minutes.