Beat egg whites and egg at medium speed of a mixer 1 minute; set aside.
Combine broth, soy sauce, sugar, and ginger in a large saucepan; bring to a boil. Reduce heat; add beef and onions, and simmer 1 minute. Add egg mixture without stirring; cook for 1 minute. Remove from heat, and gently stir. Place 1 cup of noodles in each of 4 large soup bowls, and add 2 cups of beef mixture and 1/2 cup sprouts.