In a medium bowl combine lime juice and soy sauce. Add tofu; toss gently to coat. Cover and let stand at room temperature for 10 minutes.
In a large saucepan cook the 1/2 cup green onions and the garlic in hot oil over medium heat for 3 minutes, stirring occasionally. Add water and vegetable broth. Bring to boiling. Add broccoli, carrot, and noodles. Return to boiling; reduce heat. Simmer, uncovered, for 4 minutes.
Add tofu and any liquid remaining in the bowl, the sprouts, and the crushed red pepper. Return to boiling; reduce heat. Simmer for 1 to 2 minutes more or until broccoli and noodles are tender and soup is heated through. Ladle soup into bowls. Top with peanuts, green onion tops, and, if desired, basil.