Place all the ingredients for the chicken stock in a large stockpot (at least an 8-quart) with a lid. Pour enough water to cover the chicken by a couple of inches. Place the lid on the pot and bring the water to a boil over high heat.
Once the water is beginning to boil, remove the lid or prop it a little to prevent spilling, if necessary. Lower the heat to medium-high and gently boil until the chicken is cooked through and a digital thermometer inserted into the thickest part reads 165 degrees.
Carefully remove the chicken from the pot and place in a shallow dish, like a 9x13” pan, until it is cool enough to handle and remove all the meat. Allow the stock in the pot to cool also while the chicken is cooling.
Place the cheese cloth inside a colander and place the colander inside a large enough bowl to hold the stock. Another stock pot, Dutch oven, or large bowl would be good. Carefully strain the stock through the cheese cloth, and discard all the solids. They have given their all.
Shred the meat from the chicken; set aside.
Wipe out the stock pot if necessary so it is clean to make the chicken noodle soup.
Heat the oil in the stock pot over medium-high heat until shimmering. Add the carrots, celery, and onion, and sauté until just softened. Add the garlic and stir for about 30 seconds.
Maintaining the heat, add 6 cups of the stock to the vegetables. Feel free to add more of the stock to your soup if you would like. Any remaining stock can be refrigerated or frozen for another later use. Add salt and pepper to taste and bring to a gentle boil.
Add the noodles and cook according to the package directions.
Add the shredded chicken, taste for seasoning, and adjust as desired. Serve very warm.