1. Arrange tofu on several layers of heavy-duty paper towels. Cover with additional paper towels; let stand 15 minutes. Cut into 1/2-inch-thick cubes.
2. Heat a large nonstick skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add tofu; sauté 4 minutes or until browned. Place tofu in a bowl. Return pan to medium-high heat. Add remaining 1 tablespoon oil to pan. Add onions and next 4 ingredients (through bell pepper); stir-fry 4 minutes or just until tender. Add 2 tablespoons soy sauce, 1 tablespoon vinegar, and salt; cook 30 seconds. Add mushroom mixture to tofu.
3. Stir in remaining 1 tablespoon soy sauce, remaining 1 tablespoon vinegar, quinoa, cabbage, cilantro, and sugar. Toss well to combine.