Heat the oil in a large pot over medium heat. Add the onion, carrot and celery and cook until the onion is soft and translucent, 3 to 5 minutes. Add the garlic and cook until fragrant, 45 to 60 seconds. Add the chicken stock and stir to combine. Add the bouquet garni. Bring to a boil over high heat. Reduce the heat to simmer and allow the flavors to marry, about 15 minutes.
Add the green beans, egg noodles and chicken. Stir to combine and poke with your spoon to make sure the beans and noodles are submerged. Simmer until the noodles and beans are tender, 8 to 10 minutes. Taste and adjust the seasoning with salt and pepper. Ladle into warmed bowls and serve immediately.
In a large soup pot, combine the chicken, water, celery, onions, carrots, bay leaves, parsley, thyme and peppercorns. Bring the mixture to a boil over high heat.
Decrease the heat to low and simmer for 11/2 hours, skimming the foam off the top as it rises. Strain through a colander, reserving the stock and discarding the chicken and vegetables.
Cool and store in an airtight container in the refrigerator for up to 1 week, or freeze for up to 3 months. Before using, skim off and discard any fat that solidifies on the surface of the stock.