1. Place tofu in a single layer on several layers of paper towels. Cover tofu with several more layers of paper towels, and top with a cast-iron skillet or other heavy pan. Let stand for 30 minutes. Discard paper towels.
2. Cook pasta in boiling water until al dente; drain. Combine pasta, sesame oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper; toss. Set aside.
3. Sprinkle remaining 1/4 teaspoon salt and remaining 1/8 teaspoon pepper evenly over tofu. Heat a large cast-iron skillet over medium-high heat. Add 1 tablespoon canola oil to pan; swirl to coat. Add tofu to pan; cook 4 minutes on each side or until golden. Remove from pan; cut into bite-sized pieces. Combine oyster sauce and next 3 ingredients (through vinegar) in a small bowl, stirring well.
4. Heat a wok or cast-iron skillet over medium-high heat. Add remaining 1 tablespoon canola oil to pan; swirl to coat. Add onion; stir-fry 2 minutes or until lightly browned. Add cabbage, carrot, and garlic; stir-fry 2 minutes or until cabbage wilts. Reduce heat to medium; stir in tofu and vinegar mixture, tossing to coat. Add pasta and bean sprouts; toss. Cook 2 minutes or until thoroughly heated. Sprinkle with green onions.