Heat extra-virgin olive oil in a very large pot over moderate heat. Prep the vegetables by chopping/or peeling them. Keep them in separate piles.
Add each vegetable to the pot in the order they are listed, waiting a couple minutes between each vegetable before adding the next.
Add bay leaves and season vegetables with salt and pepper, to taste. Depending on how thick you want your soup, add broth to the pot until it's the amount you prefer. Bring it to a boil.
Add diced chicken, return soup to a boil, and reduce heat back to moderate. Cook the chicken for 2 minutes and then add the noodles. Cook the soup for 6 minutes or until noodles are tender. Remove soup from the heat.
Stir in parsley and dill, remove bay leaves, and serve.