Place the chicken in a large pot and cover it with 4 quarts of water.
Bring to a boil over high heat.
Reduce the heat to low and simmer for around 30 minutes.
Carefully remove the chicken from the pot using a slotted spoon.
Once cool enough to handle, shred the meat, discarding any bones.
Melt the butter in a separate large pot over medium heat.
Add the onions, carrots, celery, and garlic.
Cook, stirring often, until the vegetables are soft, about 5-6 minutes.
Whisk the flour into the pot with the vegetables until fully combined.
Slowly add the chicken broth from the other pot, stirring constantly.
Add the shredded chicken back to the soup.
Stir in the heavy cream and egg noodles.
Cook for another 10 minutes, until the noodles are tender.