Preheat the oven to 400ºF. Line 2 baking sheets with parchment paper and place the squash cut-side down on them. Bake for 25-35 minutes, until the squash is just tender.
While the squash bakes, prepare the quinoa: Bring the broth to a boil in a medium saucepan and add the quinoa. Cover, lower heat to simmer, and cook undisturbed for about 20 minutes, until the liquid has been absorbed. Remove from heat.
Meanwhile, in a large skillet, sauté the onion and garlic with the oil over medium heat until the onion is translucent. Add the carrot, celery, and parsley and continue to cook for another 7-10 minutes, until the celery begins to soften. Add the remaining ingredients including the cooked quinoa and stir to combine well. Cover, lower heat, and cook another 5 minutes, until heated through.
Once the squash is ready, remove from the oven and turn cut-side up. Fill each half with ¼ of the quinoa mixture, then return to the oven for another 10-15 minutes until heated through. For a side dish, slice each half again lengthwise to form 2 smaller pieces.