For the squash: Preheat the oven to 400 degrees F.
Place the squash on a baking sheet flesh-side up and rub with the olive oil. Season liberally with salt and pepper. Roast until the edges begin to ripple and a poke with a fork reveals tender flesh, about 40 minutes. Allow to cool until easy to handle.
Lower the oven temperature to 350 degrees F.
Use a spoon to scoop out the flesh into a large bowl, leaving about 1/4 inch of flesh within the skin of each squash half to help it maintain its shape.
For the filling: In a large pan on medium-high heat, add the olive oil and sausage. While cooking, break the sausage into bits like ground meat with a wooden spoon. Once some of the fat is rendered from the sausage, add the onions, paprika, pumpkin pie spice, sage, celery, bell peppers and a pinch of salt. Cook until the sausage is done and the vegetables are tender.
Add the mixture to the bowl of squash along with the cheese, walnuts and cranberries and stir to combine. Taste and season with salt and pepper if needed. Fill the hollowed squash halves with the mixture and place back in the oven to melt the cheese and make the tops golden brown, 15 more minutes. Sprinkle with parsley and serve warm.