Cut steak into 1- to 2-inch pieces; heat 1/2 tablespoon of the oil in pan until hot. Add ginger and garlic; cook 1 minute. Add half of the beef; stir-fry for 2 minutes or until the outside surface of beef is no longer pink and is thoroughly cooked. 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 8–10 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.