Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.

Place squash, cut-sides down, on the prepared baking sheet.

Bake in the preheated oven until squash starts to soften, about 25 minutes. Reduce the oven temperature to 350 degrees F (175 degrees C); continue baking until squash easily pierced with a knife, about 25 minutes more. Cool.

Cook sausage in a large skillet over medium heat until browned, about 5 minutes. Transfer to a plate; reserve drippings in the skillet. Add onion, celery, and carrot to the skillet: cook and stir until starting to soften, about 5 minutes. Stir in cooked sausage, diced tomatoes, chicken broth, tomato paste, and garlic; simmer until flavors combine, about 15 minutes.

Scrape squash flesh into spaghetti-like strands with a fork; transfer to a 9x13-inch casserole dish. Stir in tomato sauce to combine; top with mozzarella cheese.

Bake in the preheated oven until bubbly and golden brown, about 25 minutes.