Bring soup stock, star anise, grated ginger and soy sauce to a boil.
Add salt and the egg noodles. Cook until al dente, 5 to 7 minutes. Divide noodles among 4 soup bowls.
Add chopped carrots, then the snow pea and green onions. Cook two minutes then add the frozen peas.
In a small cup, make a slurry by combining the cornstarch and 2 tablespoons of cold chicken stock or water. Stir until dissolved.
Slowly pour in the cornstarch mixture while stirring the stock, until thickened. Remove and discard the star anise.
Reduce heat to a simmer. Pour in the eggs slowly while stirring the soup in the same direction.
The egg will spread and feather.
Turn off the heat and add the green onions. Lastly a few drops of sesame oil.