Preheat your oven to 400°F (200°C). Cut the squashes in half from stem to end and scoop out the seeds. Brush the insides with olive oil and season with salt and pepper. Place them cut-side down on a baking sheet and roast for 30 to 40 minutes until the flesh is tender when pierced with a fork.
While the squash is roasting, heat a large skillet over medium heat. Add the ground sausage and cook until browned, breaking it into small crumbles. Remove the meat from the pan and set it aside, leaving about a tablespoon of fat in the skillet.
In the same skillet, add the diced onion and cook for 3 to 4 minutes until softened. Stir in the minced garlic, diced apple, dried sage, and thyme. Cook for another 3 minutes until the apple begins to soften. Stir the sausage back into the pan along with the dried cranberries and pecans.
Flip the roasted squash halves so the hollow side is facing up. Spoon the sausage and apple mixture generously into the center of each squash. If you are using parmesan cheese, sprinkle it over the top of the filling.
Return the stuffed squashes to the oven. Bake for an additional 15 minutes, or until the filling is heated through and the cheese is melted and slightly golden. Serve immediately while hot.