In the stockpot, combine chicken stock, star anise, cinnamon stick, and savory.
Cook covered for 15 minutes.
Add the chicken, and poach, on medium heat, until just cooked through, about 15 minutes.
Using a slotted spoon, transfer chicken to a plate.
Bring a medium pot of salted water to a boil. Add noodles and cook until al dente, about four minutes.
Strain, and place under cold running water to start cooking.
Set aside.
Heat oil in a large sauté pan over medium low heat.
Cook the leeks, celery, carrots, and garlic until softened, about six minutes.
Add Portobello mushroom.
Cook five minutes.
Remove star anise and cinnamon from broth; add broth to the sautéed vegetables.
Bring to a simmer over medium high heat.
Cook 10 minutes.
Put broth and chicken together and serve over noodles.