Preheat the oven to 400 degrees F. Cut squash in half lengthwise. Scoop out the seeds. Drizzle with olive oil and sprinkle with a pinch of salt and pepper.
Meanwhile, cook the quinoa. Place quinoa and vegetable broth in a medium saucepan. Place over medium heat and bring to a simmer. Cover and cook over low heat until quinoa has cooked through and absorbed all the water, about 15 minutes.
Add the garlic, mushrooms, thyme, and a dash of salt and pepper and continue to sauté until mushrooms are tender and their liquid has evaporated. Stir in 2 cups of the cooked quinoa, soy sauce, and vinegar.