Preheat oven to 375 degrees F. In 3-quart, shallow baking dish, toss mushrooms with walnuts, garlic, 1 tablespoon oil, 3⁄4 teaspoon salt, and 1⁄4 teaspoon pepper; spread in even layer. Bake 20 minutes or until mushrooms are tender. Set aside to cool. Turn oven off. In a food processor, pulse mushroom mixture, red onion, green onions, and vinegar until mostly smooth, scraping side of bowl if necessary. Transfer mixture to a large bowl and stir in quinoa and cornstarch until well-blended. Cover the bowl with plastic wrap and refrigerate 2 hours. Preheat oven to 375 degrees F. Line baking sheet with foil. Form mixture into 5 patties (about 1/2" thick and 3" wide). In a 12" nonstick skillet, heat remaining 1 tablespoon oil on medium. In 2 batches, cook patties 5 minutes or until well-browned, turning over once. Transfer seared patties to the prepared baking sheet. Bake 10 minutes or until hot in centers.