Preheat oven to 400 degrees F. and line a large rimmed baking sheet with parchment paper.
Use a sharp knife to cut squash in half horizontally (from tip to stem). To make it easier, pierce squash a few times with a sharp knife, then microwave them one at a time for 5 minutes. Use a spoon to scoop out the seeds and stringy pieces, and discard.
Place the squash halves on prepared baking sheet cut side up. Drizzle 1 tablespoon of olive oil on top of the squash, (or use a pastry brush to spread it on evenly), and sprinkle with ½ teaspoon of salt.
Turn squash over so that they are cut-side down. Bake for 35 to 45 minutes, until the squash is fork-tender.
Meanwhile, cook the quinoa: Add the rinsed quinoa and vegetable broth to a medium saucepan. Bring to a boil over medium-high heat, then cover and reduce to a low simmer for about 20 minutes, or until the broth is absorbed. Remove from heat and fluff with a fork.
Prepare filling: In a large skillet, heat remaining 2 tablespoons of olive oil over medium heat. Saute the shallots and celery for 5 minutes, until softened. Add the mushrooms and cook for 5-7 minutes. Add the apple, cranberries, garlic, thyme, sage, cinnamon, remaining 1 teaspoon of salt, and pepper, and cook for an additional minute.
Remove pan from heat and add the cooked quinoa and chopped walnuts. Stir to combine well, and season to taste.
Using tongs, turn the cooked squash halves over to be cut-side up again. Use a large spoon to distribute the quinoa mixture evenly between the squash, pressing gently to pack the filling in a bit. (*For a crispier top, drizzle quinoa filling with a small amount of olive oil.) Place squash back in the oven and bake for another 15 minutes. Serve immediately.