1. Prepare the noodles according to package directions; drain.
2. Combine vinegar and 1 tablespoon sugar, stirring until sugar dissolves. Add banana pepper; set aside.
3. Place tofu on several layers of heavy-duty paper towels; cover with additional paper towels. Let stand 20 minutes, pressing down occasionally.
4. Combine remaining 1 teaspoon sugar, lime juice, and next 3 ingredients (through fish sauce). Combine eggs and salt, stirring well.
5. Heat a large wok over high heat. Add 1 1/2 tablespoons oil; swirl to coat. Add garlic; stir-fry 15 seconds. Add chicken; stir-fry for 2 minutes or until browned. Add pressed tofu; cook for 1 minute on each side or until browned. Pour in egg mixture; cook 45 seconds or until egg begins to set around chicken and tofu. Remove from pan; cut into large pieces.
6. Add remaining 1 1/2 tablespoons oil to wok; swirl to coat. Add 2 cups bean sprouts, green onions, and dried shrimp; stir-fry 1 minute. Add noodles and soy sauce mixture; stir-fry for 2 minutes, tossing until noodles are lightly browned. Add reserved egg mixture; toss to combine. Arrange remaining 2 cups bean sprouts on a platter; top with noodle mixture. Sprinkle with peanuts and cilantro. Serve with vinegar mixture.