Ginger Egg Drop Soup

10 green onions, divided
3 cups water
3 cups vegetable or chicken broth
1 3 to 4 inch piece of ginger, peeled and cut into 4 pieces
2 boneless chicken breasts or 4 thighs cut into bite sized pieces
4 large eggs, lightly beaten
Salt and pepper to taste
Sesame oil

Slice 6 green onions into 2 inch pieces. Place the sliced green onions and the broth in a saucepan. Add the water and ginger. Bring the soup to a boil then reduce to a simmer. Add the chicken pieces and cook uncovered for approx 15 minutes.
 
Remove the green onions and ginger from the soup. Bring the soup to a bubbling simmer but not a boil. Slowly whisk in the beaten eggs, cooking for an additional 2 minutes. Chop the remaining green onions. Remove the soup from heat, season with salt and pepper to taste and stir in the chopped green onions. To serve drizzle a little sesame oil over the top of each bowl.