Preheat oven to 375°F and line a baking sheet with foil. Rub the flesh of the squash halves with olive oil and sprinkle with salt. Lay each cut-side down on the sheet and bake approximately 30-40 minutes (adjust to 20-30 minutes if using smaller or thinner-skinned squash, like delicata). You will know the squash is done when the flesh can be easily pierced with a fork. Remove from the oven and raise the temperature to 425°F.
Once the squash has been roasting a few minutes, start the stuffing. Heat a large skillet over medium heat. Add the sausage and fry until browned (5-10 minutes). Remove with a slotted spoon and set aside, leaving the drippings in the pan.
Melt the half tablespoon of butter in the pan and add the carrots and mushrooms. Cook until the vegetables are softened (approximately 8-10 minutes), stirring occasionally. Mix in the apple and add salt and pepper to taste, cooking 1 minute. Add back in the sausage, then the spinach, sage, and rice and cook one more minute while tossing the ingredients to combine. Remove the pan from heat.
To assemble, turn the squash over gently so that the flesh side is up. You can either use the same baking sheet for the next step, or transfer the squash to more presentable casserole dish if you plan to serve family style at the table - Whichever you prefer. Fill the cavities of the squash with the rice stuffing, heaping it as high as possible. Sprinkle the cheese over the tops of each stuffed squash, and bake for 10 minutes.