1. Preheat the oven to 350 degrees Fahrenheit. Arrange the squash halves cut sides up on a large rimmed baking sheet and rub with oil. Season with salt and pepper and turn the squash cut-sides down. Roast for about one hour, or until tender. Let cool slightly.
2. Increase the oven temperature to 375 degrees Fahrenheit. Spread the cornbread cubes on a large baking sheet and bake for about 20 minutes, until toasted. Let cool completely. Leave the oven on.
3. In a medium skillet, cook the sausage over moderate heat until browned. Transfer the sausage to a paper- towel-lined plate. Heat the fat in the skillet plus one tablespoon oil. Add the red onion and cook over moderate heat until softened, about four minutes. Add the celery, garlic and sage and cook, stirring occasionally, until the celery is softened, about four minutes. Stir in the sausage.
4. Peel the roasted squash. Transfer three cups of the squash to a food processor, add the sugar and puree until smooth. Season the mixture with salt, add the eggs and process until incorporated. Add the chicken stock and process again.
5. In a large bowl, combine the toasted corn bread with the squash puree and let stand for five minutes. Stir lightly, add the onion-kosher sausage mixture and one teaspoon of salt and stir again.
6. Bake the muffins and any extra foil-wrapped stuffing in the upper third of the oven for about 40 minutes, until crisp on top and heated through. Unmold the stuffing muffins and serve hot.
7. Generously grease a 12-cup muffin tin. Mound the stuffing in the prepared muffin cups. Wrap any extra stuffing in a piece of heavy-duty foil.