Cut steaks crosswise into 1/4-inch thick strips; cut strips in half. Heat 1/2 tablespoon sesame oil in large nonstick skillet over medium-high heat until hot. Add ginger and garlic; cook 1 minute. Add 1/2 of beef; stir-fry 2 minutes or until outside surface of beef is no longer pink. Remove from skillet. Repeat with remaining oil and beef. Season with salt and pepper, as desired. Keep warm.
Add broth, green onions and mirin to skillet; bring to a boil. Reduce heat to low; simmer 8 to 10 minutes.
Meanwhile divide noodles and beef evenly among 4 large soup bowls.
Bring broth mixture to a boil over high heat; ladle boiling mixture evenly over beef and noodles. Garnish with carrots.