In medium saucepan, heat oil over medium-high heat. Stir in half of green onions, and add ginger, garlic, and pepper flakes; cook 1 minute. Stir in chicken broth and bring to a boil; reduce heat and simmer 5 minutes. Cover and keep broth warm on low heat.
In large bowl, combine noodles, carrots, and snow peas. Pour 4 cups boiling water over noodle mixture, and let sit 10 minutes. Drain well and place noodle mixture in individual bowls. Divide beef, radishes, and remaining green onions among bowls. Pour hot broth into bowls. Garnish with cilantro and mint, if desired. Serve with lime wedges.